Have you read the blog post linked above? The blog owner isn't making that argument -- in fact, she's said repeatedly that she believes he was born in the U.S.
If you read the material, including American Expat's post (linked at the link), you'll find that the questions are a) whether he was a citizen of Indonesia through adoption; b) whether he gave up or renounced that citizenship when he achieved the legal age of 18; and c) whether he ever traveled, as an adult, on an Indonesian passport as an Indonesian citizen; and d) if the answer to any of the above is affirmative, has he deliberately attempted to conceal the fact(s)?
"The concept of dual nationality means that a person is a citizen of two countries at the same time. Each country has its own citizenship laws based on its own policy.Persons may have dual nationality by automatic operation of different laws rather than by choice. For example, a child born in a foreign country to U.S. citizen parents may be both a U.S. citizen and a citizen of the country of birth."
"A U.S. citizen may acquire foreign citizenship by marriage, or a person naturalized as a U.S. citizen may not lose the citizenship of the country of birth.U.S. law does not mention dual nationality or require a person to choose one citizenship or another. Also, a person who is automatically granted another citizenship does not risk losing U.S. citizenship. However, a person who acquires a foreign citizenship by applying for it may lose U.S. citizenship. In order to lose U.S. citizenship, the law requires that the person must apply for the foreign citizenship voluntarily, by free choice, and with the intention to give up U.S. citizenship."
Answer to am b, c and d: Irrelevant under US law whether true or not. Possibly interesting from a political standpoint in re how voters might view such actions. But utterly irrelevant from a legal standpoint.
It does not matter whether Indonesia consider(ed) him a citizen, now or in the past. A parent cannot renounce US citizenship for her child. Only an adult US citizen can do so, and it requires quite specific actions, which nobody has claimed Obama ever did.
You cannot unintentionally or accidentally void US citizenship. This is by the law’s design.