I've generated so many worlds searching for an animal person with available religion that I think it must be bugged then. I'm going to test some Elf-only high savagery worlds just to make sure though. I think that should get me some decent sized civilized animal-person pops.
All the other non-standard civ members, including integrated experiments, seem to pick up religion in at least one site in every world I make, but never, ever, an animal person.
-Elf-land test:
I have a site in a 200 year-old elf world in which 409 cardinal men currently reside. They've been arriving dozens at a time since the year 86. Elves in the site all worship one of 3 different forces. Cardinal men get none.
169 hedgehog men, living in harmony with elves at their forest retreat, no religion. Same site has hundreds of kangaroo men and cardinal men too. All living there for at least 50 years. No religion despite presence of a force for all elves to worship.
(Yes, elf force religions spread happily to regular races).
And even with a pantheon, no difference. 100 elven gods to worship. But the population of Cleanpack (185 red squirrel men since 77 years ago, 191 two-humped camel men since 50 years ago) only allows elves to have religion (and would allow other civilized races including experiments to worship, but this world doesn't have any)
*Although, please note that it could be just the Adventurer menu that's at fault rather than adoption of religion by animal people*