Indonesia didn’t allow for dual-citizenship during the time Obama lived there. However, Indonesian citizenship law at the time stated the ways that someone could become naturalized in that country and what they would have to do to lose that citizenship.
The law in question is Law No. 62 of 1958, “Law on the Citizenship of the Republic of Indonesia”, 62/1958 for short. Assuming an adoption took place, it would fall under Article 2 of that law.
“Article 2.
(1) A foreign child of LESS THAN 5 YEARS OF AGE who is adopted by a citizen of the Republic of Indonesia acquires the citizenship of the Republic of Indonesia, if such an adoption is declared legal by the Pengadilan Negeri at the residence of the person adopting the child.” [Barack Obama did not move to Indonesia to live at the residence of Lolo Soetoro until he was 6 years old.]
Note the age limit in the law - “less than 5 years of age.” Lolo Soetoro married Stanley Ann Dunham in 1965 IN HAWAII. Stanley Ann Soetoro and Barack Obama didn’t move to Indonesia until October, 1967, when Obama was already six years old.
Under Indonesian law there was no way via adoption that Indonesian citizenship could have been granted to Barack Obama.
No one has been able to come up with any documented evidence of an Indonesian adoption, the acquisition of Indonesian citizenship or a renunciation of U.S. Citizenship.
It’s unfortunate you ignored Article 4 of Law No. 62, 1958 which applied to Obama and not Article 2.
Article 4.
(1)A child outside a marriage of a mother who is a citizen of the Republic of Indonesia or a child out of a legal marriage, but who has in a case of divorce been assigned to the care of its mother, a citizen of the Republic of Indonesia, who follows the nationality of the father, a foreigner, may present a petition to the Minister of Justice in order to acquire the citizenship of the Republic of Indonesia, if, after, having acquired the citizenship of the Republic of Indonesia, it possesses no other nationality or states at the same time to have released another nationality according to the procedure stipulated by the legal provisions of the country of origin and/or according to the procedure stipulated by the agreement on the settlement of the bi-nationality between the Republic of Indonesia and the country in question.
Obama’s mother obtained Indonesian citizenship through Article 7:
Article 7.
(1)A foreign woman married to a citizen of the Republic of Indonesia, acquires the citizenship of the Republic of Indonesia, if and when she makes a statement as to that effect within 1 year after contracting said marriage, except in case when she acquires the citizenship of the Republic of Indonesia she possesses still another nationality, in which case the statement may not be made.
(2)With the exception as mentioned in para 1 the foreign woman who marries a citizen of the Republic of Indonesia also acquires the citizenship of the Republic of Indonesia one year after the marriage has been contracted, if within that one year her husband does not make a statement as to release his citizenship of the Republic of Indonesia.
Said statement may only be made and only results in the loss of the citizenship of the Republic of Indonesia if by such a loss the husband does not become stateless.