Hell, just read Toynbee. Rome didn't collapse because of problems relating to homosexuality. It collapsed because it was a militaristic society that got too big for its britches, and because the Roman central authority depopulated the provinces through taxation. See, Italy was exempt from taxes, so all the funds for running the empire had to come from the conquered territories. When Rome hit its boundaries and couldn't expand anymore, it was unable to loot these conquests for cash, which put a big crimp on an Empire based on paying soldiers to fight. Couple that with the Volkwanderung creating a huge amount of pressure on the borders, the only source of income came from taxing the provinces into oblivion. Eventually, when the Imperial government couldn't pay the legions any more, they would go around on their own extorting money from towns and villages.
Finally, people just left the cities because then they could avoid the tax collectors, as it's hard to track people down in a sparsely-populated countryside. Disintegration proceeded from there.
The oft-claimed "moral collapse" of the Roman Empire is just silly. People who say this are just repeating nonsense they've heard passed down from ignorant moralist to ignorant moralist. Hey, since the Empire converted to Christianity more than a hundred years before the West collapsed, what would such a theory say about Christian morality?
What's ironic is that Rome was far more moral in a Christian sense during its final decline than at any other time. Its most libertine period was the early time of its greatest glory. If it had any impact at all, Christianity actually hurt Rome by destroying families, because many noblemen decided to enter monasteries instead of making heirs, so many great houses went extinct. There is even a story about a young noblewoman who was Christian and decided to remain celibate. She had a hard time convincing her young husband, but when their only child was stillborn, he converted. They spent the rest of their days living as siblings and giving away all their inherited wealth to build monasteries and feed the poor (the story is also a testament to the incredible wealth enjoyed by the small upperclass in Rome).