Ben Carson's Muslim President Comments and the 1788 Debate in North Carolina Over Ratification of the Constitution

So Ben Carson said he wouldn’t support a Muslim for President and Islam is inconsistent with the Constitution. Watch:

Then he said he might vote for a Muslim for Congress.
This was such an easy question that I am surprised Carson botched it up.  Even if you personally would not vote for a Muslim, the Constitution prohibits a religious test so it doesn’t matter what Ben Carson’s opinion is. All I can figure is he wanted to bounce with anti-Muslim sentiment.
The issue of a Muslim (Mahometan) president came up during the North Carolina Debates over ratification of the Constitution in 1788 (to read it all keep clicking the next image). The defenders of the Constitution indicated that religious liberty would not prevent a Muslim from running. Being elected however, is another matter, and according to one delegate would require a major change in public sentiment.
Speaker James Iredell, appointed to the Supreme Court by George Washington in 1790, answered worries that a pagan or Mahometan might gain office:

But it is objected that the people of America may, perhaps, choose representatives who have no religion at all, and that pagans and Mahometans may be admitted into offices. But how is it possible to exclude any set of men, without taking away that principle of religious freedom which we ourselves so warmly contend for? This is the foundation on which persecution has been raised in every part of the world. The people in power were always right, and every body else wrong. If you admit the least difference, the door to persecution is opened. Nor would it answer the purpose, for the worst part of the excluded sects would comply with the test, and the best men only be kept out of our counsels. But it is never to be supposed that the people of America will trust their dearest rights to persons who have no religion at all, or a religion materially different from their own. It would be happy for mankind if religion was permitted to take its own course, and maintain itself by the excellence of its own doctrines. The divine Author of our religion never wished for its support by worldly authority. Has he not said that the gates of hell shall not prevail against it? It made much greater progress for itself, than when supported by the greatest authority upon earth.

He added later:

It is apprehended that Jews, Mahometans, pagans, &c., may be elected to high offices under the government of the United States. Those who are Mahometans, or any others who are not professors of the Christian religion, can never be elected to the office of President, or other high office, but in one of two cases. First, if the people of America lay aside the Christian religion altogether, it may happen. Should this unfortunately take place, the people will choose such men as think as they do themselves. Another case is, if any persons of such descriptions should, notwithstanding their religion, acquire the confidence and esteem of the people of America by their good conduct and practice of virtue, they may be chosen. I leave it to gentlemen’s candor to judge what probability there is of the people’s choosing men of different sentiments from themselves.

Iredell saw that the Constitution does not require Christianity to be the national religion. A president of a non-majority religion might be elected if voters become less Christian or because an individual of a minority religion displays trustworthy character.
In any case, Iredell made it clear that Christianity ought not depend on the support of Constitution or any other worldly authority.
Carson’s later came out and said he didn’t oppose a Muslim running for office if the candidate rejected Sharia law.
The next question to ask Carson is if the Constitution is flawed since it forbids a religious test.