US citizens weren't barred from entering Pakistan in 1981- the State Department had a travel advisory for Pakistan, but there was no law, either Pakistani or US, preventing a US citizen from traveling to that country.
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.