When I visited Dubai a couple years ago, they never asked about my religious views at all. It's not on any form they give you, it's not on my passport and travel documents, and they never verbally asked me. So getting through immigration won't be a problem.
Also, Dubai is filled with non-Muslim workers, mostly Filipinos, Indians, Brits and Americans. The Arabs there prefer hiring non-Arabs for jobs they do not want to do themselves, or for specific expertise. If they had a problem with other religions, they'd have to dismiss most of their labor force, which are mostly Catholic, Protestant Christian, Buddhist or Hindu. (Many are probably secretly agnostic or secular and just say they are a particular religion just to blend into their religious culture.)
That being said, I would not recommend getting into religious discussions about atheism while there. While they allow guests in their country to be non-Muslim, they do not take kindly to someone trying to convert people to another religion (or convince people that there is no God). And posing a logical debate on the merits of atheism could be considered trying to convert someone, and possibly be interpreted as an insult to their God (i.e. Allah), since you would be openly denying He exists.
So basically, hold your tongue and you will probably be fine.