Yes, he is correct; it would be unconstitutional to prohibit a muslim from being president. On the other hand, it would be stupid to elect one.
As we have found out.
On what basis would it be unconstitutional to prohibit a Muslim from being president?
My general rule of thumb for dealing with whether or not something is constitutional was to ask myself if this argument would have worked in 1787. If it wouldn't work then, then it ought not be considered valid in the present.
It would be unConstitutional to prohibit a National Socialist, or a fascist, or a Communist from running for President in this country. The only requirements, that the person be a “natural-born” citizen, attained at least 35 years of age, and has resided in the US at least 14 years.
Apparently that “natural-born” clause has become pretty elastic, with some grave misunderstanding of just exactly what it means. Born on US soil? Born elsewhere of US citizen parent of parents? Born of non-citizen parents who have no intention of becoming citizens?