Just to clarify, by follow their religion, ATP means murdering gays. Not an exaggeration:
Given that the child rape started well before Vatican 2, I think your conspiracy theorizing needs some work, or a time machine. Though let's be honest, now I want to read this Alt history of the inquisition hunting down the lavender mafia. I might write it myself, it sounds hilarious. ATP, tell me more about this imaginary history of yours.
My bet is that the lavender mafia was simply so outrageously dressed that they could not be stopped. Only the Curches's superior interior decor could slow them, until the Inquisition could develop a fabulous new style that blew the lavender mafia away (or just blew them, historians are divided on this topic).