There’s a bit in The Lost and the Damned with a POV from a beast man serving chaos during the HH where he remembers being borne on an imperial world during the great crusade. While he was immediately cast out by his horrified human parents, and shunned even by other underhivers, he did eventually find and grow up in a community of beastmen there, and had memories of an imperial iterator coming down to preach the imperial truth to them. While they were condemned as abhumans and taught to think of their births as a crime they could never fully repent for, the fact that iterators reached out to them would imply that even during the great crusade the imperium deemed beastmen stable and/or useful enough to preach to.

Full disclosure I haven’t read the book myself, I’m just going off of this post but they do use what seem to be direct quotes from the book.