That sounds exactly as repressive and hateful that other major religion, as well as historical laws which punished homosexual acts in many western countries. You have highlighted the difference between our desires and our behavior, but you seem to deliberately avoid acknowledging that straight people are permitted an institution in which their desires can be met within constraints, but gay people are not.
"You're invited to participate in our faith so long as you scrupulously act like someone else for your whole life" sounds a lot like an unvitation.