Ha! No, there is no truth whatsoever to that. Not one iota. Not a shred. Not an atom.

Here's a thread about why the western half of the empire fell with a neat little discussion: https://www.reddit.com/r/AskHistorians/comments/t31e2/why_did_the_western_roman_empire_decline_and_fall/c4j4s2h/

Here is another thread with a fantastic discussion of Rome's decline by /u/legalaction: https://www.reddit.com/r/AskHistorians/comments/3hondg/i_heard_someone_say_recently_that_rome_destroyed/cu9cbwz/?context=3

Short answer, it's about tax and economics, bad foreign policy, recruitment problems, Huns, some really substandard emperors, and a smidge of climate change, all mixing together to cause problems so big the WRE couldn't take it and slowly crumbled - not because some men were sleeping with other men.

If I had to guess why this person thinks something so absurd, it might be that they are linking Gibbon's argument that Rome fell because of moral decay with their own views on homosexuality. A discussion about Gibbon can be found here: https://www.reddit.com/r/AskHistorians/comments/ymjth/how_is_the_decline_and_fall_of_the_roman_empire/

I hope that helps!