Such BS. The sacking of Rome by the Goths may have something to do with the fall of the empire. Some people think that lead in the drinking water from the lead pipes, made Romans looney. It also became too big to be sustainable, and the Romans could not maintain their lifestyle without conquering more territory. Also the rise of Islam may have had something to do with it.
In other words, there were many contributing factors, but homosexuality was certainly not one of them.