Can a Muslim be the president? Yes. A-6 verbatim:

"The Senators and Representatives before mentioned, and the members of the several state legislatures, and all executive and judicial officers, both of the United States and of the several states, shall be bound by oath or affirmation, to support this Constitution; but no religious test shall ever be required as a qualification to any office or public trust under the United States."

Oath: "I, [name], do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter".

Should a Muslim (or any other religion for that matter) be president?
Not if their faith overrules the supreme law of the land. See: Islamic Sharia "Taqiya" and "Kafir". Our country, our rules. Don't like it? GTFO.

I highly advise that if you care about this sort of thing to watch these two videos:

UK

Germany