No, unfortunately he is not correct. Constitution explicitly states that “no religious test” shall be applied to prevent someone from holding office.
Carson didn't day it should be a law? When voting, the voter will be the judge of that. I certainly wouldn't knowingly vote for a Muslim, one of the reasons, Romney is not president because is because he is a Mormon. Like someone else said unfortunately we appear to have already made that mistake.
Islam is not a religion, it's a political system.
We need a Constitutional requirement that Muslims not hold office in our Christian republic. I would prefer they not be allowed in. Their “faith” is antithetical to our founding principles.