Yes, technically it is. There can be no religious test. But the candidate must defend the Constitution and all Carson is saying is that he does not believe a Muslim could do that. Agree or not, Carson is essentially trying to defend the Constitution. Clearly he will be bashed endlessly for it, but he has a point.
That said, I prefer Cruz to Carson.
In Klingon in pIqaD
noH QapmeH wo’ Qaw’lu’chugh yay chavbe’lu’, ‘ej wo’ choqmeH may’ DoHlu’chugh lujbe’lu’
Translation
Destroying an empire to win a war is no victory, and ending a battle to save an empire is no defeat.