Vibrant, vital cultures though, and this in no way means enlightened or kindly ones, ten to strictly enforce sexual roles, at least below the levels of the ruling elites.
Were I to hazard I guess, I'd say that in a few generations, this will be a largely Muslim world, as that culture is becoming ever more vital, (and virulent.) And Sharia invokes death on homosexuality, again, for the common classes. So our little deviations won't really matter.
Tell, me, do you think late generation Romans, looking about them at streets buildings and institutions had a clue that in a few decades their civilization would be gone?