Indonesian laws do not control American citizenship, but actions he may have taken under Indonesian law ARE relevant for purposes of determining whether Obama affirmed allegiance to Indonesia so as to lose United States citizenship within the meaning of the INA as in effect in the early 1980s.
For example, if Obama (as a young man and not as a young child) signed and filed papers with the Indonesian government to obtain or renew an Indonesian passport, then that act alone likely constituted the making of an allegiance to Indonesia, since Indonesia required that its passport holders NOT be citizens of any other country.
In contrast, for a country like Israel which permits dual citizenship one is not required to forswear other nationalities to become an Israeli citizen and obtain an Israeli passport.
Section 349(a)(5) of the Immigration and Nationality Act (INA) (8 U.S.C. 1481(a)(5)) is the section of law that governs the ability of a United States citizen to renounce his or her U.S. citizenship. That section of law provides for the loss of nationality by voluntarily performing the following act with the intent to relinquish his or her U.S. nationality:
"(5) making a formal renunciation of nationality before a diplomatic or consular officer of the United States in a foreign state , in such form as may be prescribed by the Secretary of State" (emphasis added).
B. ELEMENTS OF RENUNCIATION
A person wishing to renounce his or her U.S. citizenship must voluntarily and with intent to relinquish U.S. citizenship:
appear in person before a U.S. consular or diplomatic officer, in a foreign country (normally at a U.S. Embassy or Consulate); and sign an oath of renunciation
Renunciations that do not meet the conditions described above have no legal effect. Because of the provisions of section 349(a)(5), Americans cannot effectively renounce their citizenship by mail, through an agent, or while in the United States. In fact, U.S. courts have held certain attempts to renounce U.S. citizenship to be ineffective on a variety of grounds, as discussed below.