No, you can't. The US has no problem with dual citizenship. The only way you might lose American citizenship in a dual citizenship case is if you actively sought the second citizenship in an effort to renounce American citizenship.
Whether or not the other country recognizes dual citizenship is not relevant.
My understanding is that the United States does allow dual citizenship, however if the nation you choose to join youself to does not allow dual citizenship, the United States respects that law and your citizenship becomes void.
However in Barrys case, when he becomes an adult at the age of 18 he can go to any foreign office of the United States and swear aleigence to reclaim his citizenship. Barry/Obama could simply produce a copy of his registration for the draft, or refer to the records of the office that he preformed this duty at.
However, to travel has he is suspected to have done at the age of 19 on an Indonesian passport is an indication that he did not do this. Which could make him invalid to run as President. Strange that this would even be an issue.
In the case of Israel, you are allowed dual Citizenship, so if you happen to make Aliah, you do not loose your American Citizenship.
In the case of Indonesia, you are not allowed dual Citizenship, so he would have to fufill the requirements of the law.
And at the age of 19, I doubt that he was very aware of his illegal actions of maintaining his Indonesian citizenship with his new US citizenship.