That's because Catholics and Orthodox have a well-proven alternative treatment for gay: monasticism. Just lock all the weirdos and losers in a walled building, dress them in uniform drab clothes and force some discipline upon them, and they won't bother you any more.
False (at least for Catholics, can't speak about Orthodox).
Gay men go into priesthood not monkhood.
Also false for the Russian Orthodox Church. Gay men go into monkhood here, but that's cos the church is run by monks. They aren't locked up anywhere, they run the place. All the sensually stimulating stuff, the money, and most importantly the right of ordination, is for the monks only. Non-monk priests and low-level monks look pretty much the same but only priestmonks can advance in rank. Monks can become priestmonks. Priests with no underage children can become priestmonks. Priests can't marry (fags love fast-tracking religious boys into ordination). Married priests with children are at the bottom of the totem pole unless they take up celebrity/adoption grifting.
Also monasteries aren't prisons, they're communal housing. Monasticism (if it weren't run by grifting fags) would be an alternative to inceldom, whoring, widowhood or post-divorce, and retirement homes. Monasteries could be good for tards to live nearby and get minded by monks, but they were never meant as tard or freak containment. Particularly, forced tonsure has never been a punishment for homosexuality.
Finally, the timeline does not hash out, the troon wave trails Protestant fag acceptance trails mainstream fag acceptance and overall decline of religion on the West. Most if not all Catholic monasteries do not accept children so a Catholic parent can't ship off a gay kid there, and a gay adult who wants to live his best sequined life can just leave the church.
What I have noticed generally with troons and Christianity, is that with Protestants and other fringe groups there are some (a minority) that will accept trooning out as a cure for being gay, but much less so for Catholics and Orthodox.
Protestants and other fringe groups often don't even need a cure for the gay, what with the openly sinning and fornicating priests.
Larger supranational churches are simply better at keeping the faith because of institutional inertia. It's easy to say the church is bad and full of faggots and the pope is satanic and you can run your own church with blackjack and hookers, but once you've allowed for changes to fundamental doctrine (because you want to make the church stronger, stricter, and less sinful), that dab of toothpaste is never going back into the tube. (To say nothing of the fact that the smaller you are, the easier it is to flat out destroy you.)