Obama, like many Americans, is a Christian.
Many people point to the fact that Obama told the media that Park51 developers had "the right" to build the so-called "ground zero mosque" 300 yards from the 9/11 memorial site.
The separation of church and state, and the right to religious freedom does allow the group to build there - and simply stating that fact does not a muslim make.
Obama was visibly irritated during a TV interview. Of the various rumors regarding his religion "The facts are the facts. We went through some of this during the campaign – there is a mechanism, a network of misinformation that in a new media era can get churned out there constantly. If I spend all my time chasing after that then I wouldn't get much done."
He also said he can't go around with his birth certificate plastered on his head.
I guess I can see where Obama would be getting frustrated with all the rumors surrounding him. However, no matter what when you are a politician you are going to have opposition, and rumors will be spread about you. At least Obama appears to be able to handle it.