And if it eventuates that he was listed as "Moslem" on any of the aforesaid docs -- BC (as revised at the time of his adoption), or renaturalization documents, or collegiate docs -- then he just has a first-rate political ineligibility as the "secret Moslem" fans cry in unison, "Aha!!"
Dual-citizenship is not recognized by the US from what I understand so it would be irrelevant. Nor would I think that another country allowing a US citizen to use its passport (without a renunciation of US citizenship) has any impact on US citizenship. Only acts of this nation can affect US citizenship.
Political difficulties from being Moslem are a different issue but would not affect his eligibility legally. Nor would his adoption.