Betcha' there are some varieties of Islam that are NOT welcome there ~ in fact, they don't even consider them Islam.
The point is, Dubai is very much a bigoted and closed society compared to the United States. Dubai supporters gush about its tolerance and acceptance of foreigners without bothering to place this praise in context. Dubai appears tolerant and open ONLY when compared to the average Islamic country.
For the UAE to sniff and complain about US "bigotry" and xenophobia is hypocritical and hollow. When US (or any) Christians seek emigrate to the UAE with the same desire and ease that middle eastern Muslims seek to emigrate to the US, I'll lift the label of hypocrite from the UAE. Not one day before.