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.
If he did not renaturalize on his return to Hawaii, but kept his Indonesian papers and passports, he'd have a hard time selling anyone that he was still NBC. I think that that is his real issue -- he used his Indonesian passports beyond age 21 and applied as an Indonesian citizen for certain collegiate benefits. If he did that, I think he has legal as well as political problems.
His adoption would not cause any NBC difficulties, I've been assured here in FR, as long as he renaturalized timely on his return from Indonesia. His father, I was told, could not alienate him as a minor on the father's own motion, as long as Barry renaturalized on his return. (And it isn't certain that he did -- his family were Reds and Bohemians, after all. His mother apparently kept her married name -- spelt "Sutoro" by her -- and her Indonesian citizenship until her death.)