As long as a person is born with American citizenship and none other, his citizenship is natural, Naturally
Yes, a Muslim can be president. Americans can choose to elect a Muhammad and descend the country into the Pitts of hell, forcing women to wear burlap bags, and stoning them, should they choose to do so.
a muslim president would probably not be so obvious. He would place members of a terrorist group in the WH, pentagon, tate department etc.
His secretary of state ould have a terrorist group connection to her highest ranking assistant.
He would support muslims against our traditional and loyal allies.
He would not stop a muslim country from obtaining a nuclear weapon even when it has threatened one of our allies.
He would make public statements supporting islam and conduct holiday services in the WH.
and so on and so on