Well one thing to keep in mind is that each individual within the denomination of any religion won’t have the same view of the denomination. While Many religious people share the same feelings toward their denomination we can see that every single human is not exactly the same.
Perhaps one can ask for example , did any Popes of the Catholic Church or did any bishops or Cardinals or nuns for that matter work for equality for LGBT folks. And considering the massive amount of these religious figures that existed through history such a search would be extensive and require some time . It could be very interesting to see the results
Here's my source. The Lollards were fairly radical and they likely saw the shunning of the temporal world as a path to salvation. That's why they were believers in apostolic poverty - the philosophy that godly men should live in poverty as did Jesus. In any event, here's the relevant excerpt from the article:
"In the Lollard Sermons, virginity is hailed as the highest form of sexuality, but marriage is necessary and sex — purely for procreation, they argue — cannot be avoided. The father of the Lollard movement, John Wycliffe, explains in his work Trialogus that marriage must be between a man and a woman and “cannot exist where there is no possibility of procreation.” In 1395 [...] Wycliffe’s followers posted The Twelve Conclusions of the Lollards. In this document, the Lollards accused the clergy of rampant sodomy, at times even hurling the term “sodomite” as a general insult. The Church, in turn, accused the Lollards of sodomy. The Lollards not only directed their accusations at clerics, they also fueled a climate of antisodomy in established institutions such as temporal courts. "
I should add that the Church very frequently accused the supporters of apostolic poverty of sexual deviancy. The Cathars, Dulcinians, and to a lesser extent, Minorites, were all accused of sexual deviancy. Apparently the Church saw a link between anti-establishmentarianism and sexual subversiveness. If you want to get immersed in that fascinating dispute then I recommend reading Umberto Eco's The Name of the Rose. It is technically historical fiction but the novel's setting is a carefully reconstructed North Italian Benedictine monastery.