As far as I know, Obama traveling on an Indonesian passport would have exactly zero relevance to his status as an American citizen.
If Chad or Thailand or Paraguay chooses to issue me a passport, it doesn’t invalidate my American citizenship. The only way one can lose native American citizenship is to formally denounce it as an adult. A parent cannot renounce citizenship for a child.
You're right. I actually hold passports from three countries (including the US). Perfectly legal, and it in no way impacts my American citizenship.