The State Department (as well as the Immigration and Nationality Act) disagrees.
It doesn't matter if Indonesia recognizes dual citizenship, since U.S. law governs U.S. citizenship. Section 349 of the Immigration and Nationality Act specifies several ways that a U.S. citizen can lose citizenship. All of them require an intent on the part of the citizen to renounce citizenship, and most require that the citizen be at least 18 years old. The only way a minor citizen can lose citizenship is by making a formal declaration of renunciation.
Right now there's no legal evidence that Obama ever had U.S. citizenship to renounce, so the U.S. law doesn't necessarily apply. Further, under the same Supreme Court decision that would supposably make Obama a native-born citizen, it was acknowledged that the parents COULD renounce the citizenship of the child.
Minors can not make that decision. Especially at the age of 3! When the marriage occurred.
Simple passport records would clarify this. Too bad they were compromised in 2008.
In the meantime. We know the Obama came off SADs passport in 2008. Did he go onto to his own passport? Did he obtain an Indonesian passport?
He was in Hawaii in 1969 and returned in 1971 so he traveled after the removal from SADs passport. What nationality did he travel under?
If he was still considered a US citizen AND entered the US after 1968 he would have HAD to present a US passport.
And of course by birth to a British National Obama - to this day - can claim British Citizenship.
Unfortunately, Obama’s life is a case study of what a natural born Citizen is not. Down to being a British Subject at birth.