The people who have least to worry from the state paranoia are the privileged classes, races, and ethnicities (ie. wealthy whites). But if you're part of the non-white underclass (nevermind Muslim), you can bet the post-9/11 paranoia and increased vigor of the police state is going to be of some concern (sometimes to the degree of fleeing the country if you're able).

Something similar is probably the case in Dubai. If you're wealthy enough, and/or have enough connections, you're probably not going to have to worry too much (except maybe about the polluted beaches, if you insist on taking a dip in the sea outside your hotel room) as long as you don't try to interfere in their politics. But the worry of running afoul of their draconian laws and of being exploited by their oppressive system increases and becomes more legitimate the lower on the totem pole you get.