I don’t remember much about history class...but isn’t it possible that homosexuality persisted until the time the empire fell?
Well, of course it did, as it has in all societies.
In fact, Hadrian, one of the Good Emperors, was a flaming fruit who deified his boyfriend when he died.
Homosexual acts were criminalized by 250 and the punishment was burning alive before 400.
Don’t see how much more drastically it would be possible to punish such an offense.