Several people (e.g., my brother, PBS, Mike Gerson - as syndicated writer for the Washington Post, the Herald Tribute and other outlets, etc.) have implied that Dr. Carson is a hypocrite or possibly ignorant of the Constitution. This is with respect to the issue of a Muslim President of the U.S.
I'll quote Mr. Gerson in the Herald Tribute,
"...
What is the proper response from a prospective president to the question: Is being a Muslim disqualifying for the presidency?
Ben Carson answered that
he “would not advocate that we put a Muslim in charge of this nation”
because Islam is incompatible with the Constitution. The Constitution
offers a different reply: “No religious Test shall ever be required as a
Qualification to any Office or public Trust under the United States.”
Gerson here makes an inference that seems to be made by essentially everyone criticizing Carson but that I would not make. The inference is that when Carson says, '...would not advocate...', Carson means, '...should be banned from being President...' .
I see the two statements as different. To illustrate, I don't thing many people would advocate 'putting an ideologically committed Satanist in charge of this nation' (actually the President is not 'in charge' of the nation, the President serves the nation but that's another story). To me, that doesn't mean that everyone who says that is a hypocrite, just that they have an opinion. I think most of those people who would not advocate 'putting...Satanist...' would none the less agree that the Constitution does not prohibit Satanists from serving. Thus I don't find the statement hypocritical.
The fact that the issue arose for Islam is simply because some notorious and significant terrorist groups (e.g., ISIS, Boko Haram, Al Qaeda, al Shabaab) are self described Islamic organizations.
Gerson's piece for the Herald Tribute is here.