BUT, IF you are a citizen at Birth, I can't possibly see how being jerked around the world as a kid, voluntarily or involuntarily, by mom, dad, step dad, kidnappers, or whoever, can possibly de-citizenize you.
Imagine that your kid is 100% American. your spouse decides to split when kid is 5, goes to Flyspeckia, marries a Flyspeckian -- your kid's not an American any more?? She can never be President?? I doubt that you would think so.
Goes WITH THE KID -- if that wasn't understood as implied.
Obama was legally adopted by Flaky Mom’s Indonesian spouse of the moment. He then became a citizen of Indonesia and was registered as such in Indonesian schools. To my knowledge, his Indonesian citizenship was never renounced.