Muslims believe Obama is a Muslim, and they are right.
Christians believe Obama is a Christian, and they are right.
Muslims believe a son inherits his father's religion. Obama cannot renounce his Muslim religion (indeed, I'm not sure he has directly), without becoming an apostate who is required to be killed by any available Muslim. So, Muslims seem to be right: Obama is a Muslim. By birth.
Christians believe a person is Christian if (approximating here) he believes Jesus Christ is the savior. Obama says that he does. So, Christians seem to be right: Obama is a Christian. By belief.
I tend to fall down on the side of the latter explanation., But it is far from clear-cut. Obama's religion, whether Muslim or Christian, depends on the perspective of the person making the judgment.