Yes, they should, but they are not. And I believe the OP asked whether transwomen should be allowed in women’s prisons because of the feeling that this would cause distress to one group if it was allowed and to another if it was not. The question being: which group deserves more protection.
Assuming there is a universal answer for that. I think this discussion has not reached an agreement yet.
Concerning the bonobos and the chimps I am afraid continuing this debate here would be a hijack, so I found an old thread to follow that theme: here. I’ll give it a bump.