Technically, under that situation, the U.S. would be unable to protect the citizenship of such a child. That’s why they have the Hague Convetion for adoptions, but unfortunately Indonesia historically has not signed on.
Indonesia could not terminate Obama's citizenship. Obama's mother could not renounce his citizenship, and Obama, himself, as a child could not renounce his citizenship. In other words, the US protects the child's citizenship by not allowing it to be lost, renounced, terminated, or any other word you want to use.
Indonesia does not make US law, the government of the United State does and the United States, ALONE, decides who are its citizens.
Would you happen to know when the Hague Convention for adoptions was ratified by the United States?