it's not a matter of "disqualification," it's a matter of electability.<quoted text>
Good thing the president isn't a Muslim, and even if he was, how does that not quality him for the presidency?
Islam does not recognize or accept the principle of separation of Church and State. There is only one law in Islam - the religious law (sharia) is also the civil law. Supreme authority over both religious and civil matters is vested in the same person (e.g., Caliph, Sultan) One who is a devout Muslim, seeking the office of POTUS, would have great difficulty swearing the oath of office to preserve, protect & defend the Constitution's Establishment clause.
This fact in turn would pose political problems for any Islamic candidate in terms of the electoral acceptability in the minds of the voters, as a practical reality.