That wouldn't really be fleeing homosexuality, as much as legalized homosexual marriage.
Plus all those American homophobes wouldn't know to make of all the hand holding and light kissing that goes in Saudi Arabia.
Not to mention the pretty lively underground gay scene in Riyadh especially. Has a reputation for it.
Although much of it is more like men in jail than actual homosexual men.
Plus all that rape of young boys. Ridiculously common in many Arab countries.
Italy won't keep gay marriage illegal for long. I give it a decade, at most. China probably isn't so far off. Maybe Hong Kong will be first. Perhaps divisions like Beijing, Guangdong etc will do it at different times.
Incidentally, Israel as the biggest gay-supporting country - Israel doesn't perform gay marriage. It recognises them, but dos not allow them to be performed.