Actually change is the primary cause of the fall of empires. Moral decay usually preceeded the fall. Lawlessness, anything goes mentalities tend to undermine the entire society. Those that sow immorality, violence and oppression are setting the stage for their own demise.Homosexuality is rejected and prohibited as a consequence of unwarranted fear and ignorance.
Otherwise, the thread premise fails as a post hoc fallacy, as there is no objective, documented evidence that homosexuality 'contributes' to empires or civilizations 'falling.'
Indeed, civilizations fail as a consequence of fearful reactionaries unwilling to accept change; where punitive, draconian measures put into place intended to stave off change serve only to further erode society, as the reactionary regime becomes increasingly harsh, oppressive, and authoritarian.
It's when reactionary totalitarianism seeks to prohibit the change, diversity, and dissent it fears a civilization begins to decay.