I believe Obama was adopted by his Indo-Nesian stepfather and was declared to be an Indonesian when he entered school. Did he later register as an American?
According to this case, no actions by his parents would rob him of being a native born or natural born citizen. He would have to reject that by some act such as accepting a foreign citizenship, or living as a foreign citizen abroad.
Since he lived in the US as a citizen from the age of 10 on, he wouldn’t have any requirement to re-register as an American. His mother also seems to have retained her US citizenship throughout her life.
You have a right to believe anything you choose. But there is no proof of this alleged adoption, and according to U.S. Law, a child cannot renounce his U.S. Citiizenship -- and we are talking of a child who lived in Indonesia from approximately age 6 though 10 -- hardly an age where a child can be held responsible for such an important decision.