Not that it makes much difference to his political behavior. He would still advance the same anti-American, pro-Islam goals either way.
Also his killing of some Jihadists with drone- and air strikes is not at odds with his Muslim identity. Muslims kill Muslims all the time. The governments of middle east countries have run their own anti-terror operations for decades.
Moreover, for Obama, the antics of ISIS and AQ are troublesome because they provoke real opposition and open peoples' eyes (temporarily) to the Islamic menace. Far preferable for BHO is the quiet continued large-scale immigration of Muslims to the USA, coupled with continued islamification of public life under "multiculturalism".
I agree. Obama is an atheist. But since Islam is more political than religious, he “believes” in it because it produces a result he embraces.. The destruction of Western Civilization.