I forget the study. But I've seen research to show that in countries where homosexuality is illegal, they have big problems with gays molesting children. There's child prostitution. In liberal countries where gays are allowed to get on with it and aren't shamed for the proclivities these problems largely disappear. They become rare events. That's not gay bashing or gay shaming. That's just what happens when you force normal and otherwise well adjusted people to live a lie. Children will always be vulnerable to desperate people.
Can that be tied to repression of homosexuality as opposed to repression of sexuality in general, though? I'm unaware of any "liberal and open about heterosexual sex but conservative and repressive about homosexual sex" countries out there. I do get the whole "sexual repression breeds perversion" thing, but I don't see why homosexuality would be a key factor in your example as opposed to it being an irrelevant factor.
And it's not just gays. The Catholic church produces broken people. Everybody who has grown up Catholic has bizarre shame based hang-ups around sex. The weirdest kinky girls I've ever had sex with have all been Catholic. I do not think that's a coincidence. It's as if the Catholic church is designed to create sexually dysfunctional people. All that shame is not healthy for anyone. Imagine growing up in an entire Catholic culture? How fucked up would those people all get?
That is a good point about what would distinguish it from the other organizations I brought up. I fail to see, however, why homosexuality would be some kind of important factor in all that as opposed to not being a particularly relevant one. If it just so happens that Catholic society has gay men gravitate more towards the priesthood and it just so happens that the repressive nature of living as a priest in the Catholic Church breeds sexual perversions such as child molestation, then there would be a correlation between gay priests and child molesters. That is very different, however, than making the statement that their being gay is one of the causative factors in that molestation.