How interesting! I'm no historian, and I don't have a firm opinion on why the Western portion of the Roman empire fragmented and eventually fell apart. I do think, however, that multiple factors played a role, from the sort of dysfunctional theocratic politics you mention, to economic stress owing to the inevitable end of the age of conquest and expansion, to military pressure related to surging migration (invasion) of Germanic and central Asian peoples.

I guess I would have to doubt that Christianity played THE role in the fragmentation of the Western empire, informed by the reality that the Eastern Roman empire centered in Constantinople thrived for many more centuries under stern theocratic rule that doesn't seem substantially different from theocratic rule in the West.

But either way, the idea that homosexuality or other sexual "immorality" caused the fall of the Western Roman empire is dismissed by historians, and I think quite rightly so.