Putting aside the admittedly emotional elements surrounding Muslims, it reminds me of the statement often fronted by Christian Fundies in defense of their most theistically infected standard bearers: "A person’s religious belief has no effect on their competence of holding that office".
An atheist candidate would have no supernaturally driven agenda. There could be no split allegiance between upholding the laws of man (Common Law / the Constitution), and some "Higher Moral Authority" handed down by some fictional divine being or prophet. There is only The Law… and evolved human ethics and culturally accepted morality. Unlike theists, there is no conflict of allegiance in the atheist mind, and no chance of decision making being based on prophesy or bizarre doctrine that welcomes or hastens Armageddon, or that may offend the sensibilities of a mythical supreme being, or that is “interpreted” as having been God Sent.