We all know people who want to paint the president as a crypto-Muslim, sent here to undermine our good Christian Nation. These people are, of course, idiots. Unfortunately they are also idiots with precedent.
Thomas Jefferson had to be secretly a Jew or a Muslim, according to source no less prestigious than John Adams, when in fact he was more of a Unitarian.
John Kennedy had to public defend his qualification to be president in spite of the fact he was something that most Americans at the time did not consider a "real" Christian - a Catholic.
Mitt Romney is a Mormon, and Ben Carson (who seems to be throwing stones of late) is a Seventh Day Adventist, and Representative Kieth Ellison of Minnesota is, in fact, a Muslim.
The US Constitution is very clear about the separation of Church and State. You know who came up with that term? A Baptist. The phrase "[A] hedge or wall of separation between the garden of the church and the wilderness of the world" was first used by Baptist theologian Roger Williams, the founder of the colony of Rhode Island, in his 1644 book The Bloody Tenent of Persecution. He founded Rhode Island, by the way, to escape persecution from Catholics in Maryland.
Evangelical Protestants were the ones who wanted the State to stay our of the Church's business and, as a protection against corruption of the church, visa versa.
Religious freedom for all is a very important right.
Beware of people who want government positions who would deny anyone that right. Even if you agree with them otherwise.
Soon enough the shoe will be on the other foot and you will be glad you did not support a precedent for religious persecution.