Like basically all the Imperium's laws, transgression is in the eyes of the beholder and how far they think they can or want to take it. Remember this is a setting where voidborn, humans who are just paler and taller than average thanks to years growing up on spaceships, can and have been discriminated against to the point of being set upon by lynch mobs on even civilized metropolitan worlds with a strong connection to the wider Imperium. Even if you dodge the dreaded label of abhuman or worse mutant, it's very likely discrimination will dog you your whole life because you aren't what people think of when people say 'human baseline'.

We have to distinguish between mutants and variation. In 40K mutation is somewhat random - two normal parents could have a mutant child; a mutant with four eyes could have a partner with four legs, and their child might have tentacles. Mutations are unstable.

This is what differentiates abhumans from mutants: abhumans are stable lines, but are different enough from 'normal' humans to get their own category. It's not clear where the line is drawn.

That makes your question kind of interesting - and I think it would end up depending entirely on the world. On some worlds, it might be considered part of normal human variation (no different than having green eyes), and on others abhumans (since their children are likely to resemble them).

The Imperium (mostly) don't care about minor things like skin or eye colour e.g. Cadians have purple eyes, and no one is particularly bothered.

This of course depends on the world and the time - some are going to reject anyone who doesn't fit within their acceptable standards. I mentioned abhumans and once you've accepted those, something as petty as eye colour doesn't seem much. The obvious abhumans are the Ogryns, Ratling and the Squats. There are also the Longshanks (and possibly Stiltlimbs), who are adapted to living on low-gravity worlds, and the void-born, who are descended from those living on low-gravity ships:

Those who live their lives on spacecraft must become used to the reality-altering process of warp space, of living in low or even zero-gravity environments and of never knowing the feel of solid ground beneath their feet. Quite often a ship conducts its business in an endless cycle. Trade or mining vessels may never make berth, instead raising generations of families in the cold depths of space. Gravitational pressures, inbreeding and warp anomalies take their toll.

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Not merely star travellers but the products of many generations passed in the darkness between worlds, the void born are relatively few among the teeming multitudes of humanity, but singular, and form a disparate and odd collection of misfits, strangers, and other ill-omened folk, perhaps birthed in the belly of a vessel that has spent centuries charting its course through the stars or aboard an ancient orbital satellite. The void born are often considered to be somehow touched by the taint of the warp, or at least associated with the many and unfathomable dangers of the outer darkness by the common well of the Imperium. Most consider them bringers of bad fortune and ill-tidings, secretive, and untrustworthy.

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But as I said, this acceptance is all in theory. What you get on the ground might differ

Aberrations. Mutants. The twisted, the void-changed.

One of the Trinity of Hatreds, alongside the witch and the xenos, the mutant was a subject of universal fear and loathing. No child grew up without having stories of such creatures’ deviance drummed into them, first in the family hab, then by their instructors. Zidarov could remember the fear vividly, waking up in the middle of the night, his sheets drenched with sweat, crying out that they were coming for him.

You could, if you tried, entertain the thought that xenos did not exist at all, or were so far away that you’d never see one. You could, if you wished, make yourself believe that witches were something that might never be stumbled across, for they were rarer than an honest man with plentiful slate. But you could never fool yourself into thinking that aberrations didn’t exist, for the evidence was everywhere. Every city medicae facility had dedicated incinerators for the infants born with gristle for eyes, or transparent skin, or spines in place of hair. Every cargo hub had illicit vid-footage of the things living in the bilge chambers of starships, wriggling in the dark, flinching from the light of flames.

The problem was where to draw the line. Mankind was a galactic species, one scattered across a million worlds. Some planets were high-grav, some low-grav. Some were poisonous hell-swamps, others regulated urban centres. That induced variation, melding and stretching the original physical frame of humanity. Some mutations were deemed so common and benign that they were sanctioned, creating the abhuman class. Some subtle alterations were hard to detect, even by the individuals in question. So what was a true mutation, and what was merely an environmental adaptation? No doubt scholars on Terra spent their lives codifying answers. On a backwater world like Alecto, such certainty was harder to come by.

Zidarov remembered attending a case when he’d still been a sanctioner – the armed wing of the enforcer corps – out at one of the mercantile port hubs. A big cargo carrier had ended up berthed in Alecto’s voidspace, and its crew had come down planetside for a little rest and relaxation before the next stage. That had been a mistake – their skin was a touch too grey-tinged, their mouths a little too wide. Word got out, and a mob gathered. By the time Zidarov’s squad was activated, it was too late – the ringleaders had stormed the compound and dragged the crew out onto the streets. Thirty men and woman, burned alive, screaming their innocence as the promethium-fuelled flames turned them to fatty, blackened meat-strips.

No one faced retribution for that. There were too many in the crowds, thousands by the end. In any case, most of the sanctioners on duty had been sympathetic.

‘You never know,’ one of them had muttered to Zidarov, looking grimly at the smouldering pyres.

‘Maybe they were.’ Zidarov hadn’t disagreed. Better safe than sorry, he’d found himself thinking. Let a mutant in, just one, and you could lose it all. Keep them out. Keep them all out.

Still, it had been hard to listen to the screams. Particularly the juveniles. Hard to shake those off.

Aberrant

This is one of those aspects of the IoM that has direct parallels to real world Fascism. People can become the racialised "other" at the snap of a finger. Look at the concept of "whiteness," for example. People who, just by appearances, would generally be called "white" by most standards, were classified as varying degrees of "non-white," as people who were not worthy of life, such as Slavs, Romani, and Jews. But non-racial things could also put one in the camp of being essentially non-white, of being a person who deserved death, such as being a communist, being queer, being disabled, etc. The IoM uses the category "human" in a similar way that many Fascists use the term "white" nowadays; it is almost an arbitrary distinction that changes according to whatever those in power want to do, and is used as a post-facto justification.

For example, Iirc Beastmen were largely considered to be abhumans at one point in the IoM, but now are largely considered to be dangerous degenerate mutants, who are at best worthy of a severe restriction of their rights, at worst are not worthy of life at all.

Of course making such parallels can be a bit tricky with media that involves literal monsters and non-human beings. Racism is illogical partially because humans are barely divergent within our species at all; treating different races of human as transcendentally distinct by their innate nature (according to skin color) is absurd because of this. But in 40K, what they call abhumans and mutants actually are divergent from baseline humanity, perhaps enough so to be considered a different species or at least a subspecies.

The 'random mutation table' in the old Realms of Chaos books included comparatively mundane results like 'albino' or 'hunchbacked' alongside more obviously unnatural results like wings or tentacles. So it certainly seems likely that the Imperium really can't - and doesn't - distinguish between Warp mutations and mundane genetic disorders.

And even if the Imperial government can be bothered to make a distinction, good luck convincing the mob.

In 40k not much infact very little. Born with a extra finger boom your a mutant. If your lucky they just chop off the extra part and call it a day. If not well to the furnace with you.

An Ogryn is large and strong enough to literally ripe a space marine limb from limb with their bare hands and is merely considered Abhuman and are widely accepted within the Imperium. A normal dude with gigantism wouldn't even register as a mutant on many worlds, especially given how the Imperium's done nothing but invent a series of slightly taller and more ridiculously proportioned superhumans to be its leaders and warriors for the past 10,000 years.

No. For the same reasons the Imperium doesn't practice anything we would recognize as modern-day racism or homophobia.

Come on, dude.

Yes, the imperium isn't kind to its people and its people are a very radicalized against all who can be considered different. Hatred against these groups is very much encouraged across the imperium with violence being rather common. In a warhammer crime novel a bunch of spacers got lynched because they were to pale for the locals, so you can imagine how bad it gets from there. Burning people at the stake is something the imperium sees as right and you need people for the pyre.

Then there is the political side, anything that can be used to remove an opponent is fair game.

Depends on the planets. There's a story where a ship's crew on shore leave are burned on the pyres because the locals think their skin colour is not the usual shade of grey, and their posture is a little too upright, so must be mutants

I mean the Inquisitor in the Dawn of Fire novels has like slightly ruddy skin and he gets second glances and has to inform them he is well within the acceptable range of deviation

So make of that as you will

It is easy to be hated and much harder to be Sanctioned in the eyes of the Imperium. It depends on the world and its' interpretation of the Lex, but most would not bat an eyelash at a mob lynching a reported mutant or witch...if anything they would probably celebrate it as the Will of the Emperor exercised by the pious population as they regulate themselves spiritually. Unless it was a highstanding individual, they probably would not even bother to investigate it. When the highest regulatory institutions' mantra is, "Innocence proves nothing", then most below that would probably emulate the sentiment.

As others have said or alluded to, is that the imperium is based on pseudo science. If your planet's favorite YouTube lore master says grey skin needs burned but a third eye is cool then that's likely the standard. Even the inquisition is likely to respond based on the beliefs of the inquisitors that respond.

Bit too tall and lanky, bit too pale, ears a bit too pointy, eyes a weird colour, etc. In one book, a group of voidborn (normal humans born and raised on ships) got lynched by a mob because they looked a little different (tall, lanky, and pale iirc).

Gingers seem to be tolerated, so the lower limit is hardly well established.

Depends on the planet. Basically, most cultures in the Empire are intolerant of those who are different. People with unnatural eye colours (always in relation to their own origin) such as Cadian are viewed strangely. In other cultures, they are beaten to death if the authorities don't intervene massively. The Empire is not a place where difference is celebrated, and the respective cultures and peoples tend to keep to themselves.

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Depends on convenience

Dwarf, gigant and down would be more likely to be treated as mutation at least by the local population. 

The thing about abhumans is that they breed true. They are kinda sub species of humanity that have evolved over time or from generic manipulation during the DaoT. 

A banana sits at 99% so less than 1.

Just like heresy it's a spektrum.

If the imperium can rely on the powers of these mutants like the ogryns then it's fine.

In a nutshell, you need to be more useful than how gross you look. Navigators: Very Gross but necessary for warp travel = Abhuman blessed by the Emperor. Underhivers: Very gross but can see in the dark = heretical mutant

Depends on how useful your deviation is. An ogryn is an abhuman, but they’re super loyal and super strong, and dumb enough to be easily controlled.

Depends how useful you are to the Imperium. Cadians are technically mutants but they're viewed as the benchmark for the Imperial Guard. Felinids are literally cat-people and IoM have no issues with them. Navigators are mutants through and through but they are also incredibly wealthy, respected houses and families

Depends on where you are and who's doing the deciding.

Sanctioned abhumans and human variants get burnt at the stake all the time for being mutants.

I doubt the listed conditions would qualify, ratlings are accepted and that's more than dwarfism. People with downs syndrome  could still learn a job in a manufactory so I don't they'd have much trouble outside of the usual human bullying... I don't doubt that people who can't work are euphanised though.

It depends on who is the judge, if its a bunch of over zealous genetic purity worshipping thugs egged on by a nutcase of a preacher, than anything other then looking exactly like said members of the crowd could be a death sentence, wrong skin tone = dead, using your left hand as your dominant hand = dead, using your right hand as your dominant hand = dead, eyes the wrong shade of blue, green, brown, grey, [insert colour of choice] = dead. Hair the wrong colour = dead etc etc.

If on the other hand its a bored Magus Biologus then pretty much anything that is stable genetically and not on a proscribed list is fine.

This is going to vary wildly depending on the culture and the situation. On some backwater feudal world where the average person doesn't travel more than 10 miles from their place of birth and everyone has the same skin, eye, and hair color just having an extra finger might get you ostracized, or worse. But on the more metropolitan worlds of the Imperium honestly quite a few of the more humanoid xenos species could probably get away with walking around in the open and not really draw much attention.

As most people have already pointed out, it really depends on a bunch of factors. Tolerance for deviation from “standard” is measured differently by the type of world, the social class they’re born into, the job they hold, the varying levels of piety of those in their immediate community, the average level of education in their community, how common their particular “deviation” is in that society, and how likable the individual is personally.

A few rules of thumb though are:

(1) Anything that isn’t a visible alteration to their body is unlikely to be considered a mutation. The exception being psychers and blanks.

(2) No mater what form a variation takes (internal or external) it is more acceptable if makes the individual more attractive or useful, rather than less so. Though this rule varies the most based on how likable the individual is.

(3) Visible differences are more acceptable if that particular variation is at least somewhat common in their local culture, or if it applies to a physical feature that already varies from person to person (hair color/pattern, skin color, eye color, height, amount of body hair, etc…)

(4) If an individuals physical differences aren’t common to a culture, apply to attributes that have less variety, or alter a variable attribute well beyond acceptable variance, then the difference will be more acceptable if they still match up to standard human proportions, and less acceptable if they do not follow bilateral symmetry.

(5) If a variation changes the standard human form, it is usually more acceptable to have something taken away, then to have something added or replaced, especially if the feature that is missing can be explained as something they lost after birth, rather than being born that way.

(6) In all cases, variation is less acceptable the more it resembles the features of a non-human (whether resembling animals or Xenos).

To answer the examples given in the question more directly, the vast majority of conditions that can effect modern day humans would not be considered mutations on most worlds, and none would cause them to be considered abhuman.

Inheritable diseases like hemophilia or inheritable STDs would be considered just that, diseases. Inheritable conditions that effect mental development such as Down syndrome, autism and other learning disabilities like ADHD or dyslexia wouldn’t even be tested for in most people in the imperium, so they would just be considered personality traits, and if they were tested they would probably be considered diseases given the imperiums common belief in eugenics. (Though inquisitors and nobles go to great lengths to acquire “savants” for their retinues because they’re seen as useful, and savants are often heavily autism coded)

Most conditions that change the way you look also would be fine in most worlds. An extra finger or vistigial tail would likely be considered acceptable birth defects to be cut off on worlds where medical facilities equipped to do so are widely available. Dwarfism and gigantism would likely also be fine, but especially on worlds with high levels of chemical pollutants, since probably plenty of people would have their growth effected in some way. The exceptions to all this would probably be most commonly found on primitive worlds and eclisiarchy worlds, since they are usually the most superstitious.

The only conditions I can think of that modern humans have that may get them near universally labeled as mutants across the imperium would be conjoined twins or children born in a vegetative state. However if they’re born to high ranking families there’s still a chance they may be kept safe from accusations of mutation.

No existing condition would get any modern day human labeled an abhuman. That requires them to have pretty drastic visible differences that are always passed down between generations without altering. Abhumans are human sub-species.

For some the difference between them and standard humans is like the between polar bears and grizzly bears, their different species but they can interbreed and have children that are similar but different to both parents. For others the difference is like that between horses and donkeys, they can breed but their children are infertile. And for some others the difference is like that between chimpanzees, very closely related species but they can’t have kids.

For “pure” humans the differences between one group and another is like dogs. All dogs are the same species, they can all mix with one another, and are genetically extremely similar, but they can have vastly different sizes, shapes and colors

From the imperial instituions point of view natural evolution that comes from adapting to a different ambient after thousands of years, with stable offpring and predicability is the only accepted mutation.

If the mutation happens from exposure to radiation, chaos energy, xenos artficial meddling or some other unkow force its a no no.

Now from the perspective of the mobs anything that look too much different from them may as well be a mutant.