One of these religions is not like the others.
Islam isn’t in America to be equal to any other faith, but to become dominant. The Koran, the Muslim book of scripture, should be the highest authority in America, and Islam the only accepted religion on Earth.-Omar Ahmad, founder of the Council on American-Islamic Relations
It's ironic that Progressives who reference Jefferson's "wall of separation between church and state" to bolster their case supporting abortion should consider Ben Carson's rejection of sharia discriminatory.
The Constitution's Article Six prohibits a religious test as a qualification for any public office, but that same document contains a First Amendment forbidding the federal government from establishing a national religion. An Islamic president would, by definition, either be an apostate (i.e., a lapsed Muslim according to main-stream Islamic theologians) or refuse to enforce the entire Bill of Rights.
Appealing to the Constitution when you deny its primacy in American law is not merely hypocritical, it's taqiyya for the dhimmi.