“He’s a lawyer now - back in the US. Under your interpretation - he is a natural born citizen AND NOT an Israeli citizen. “
Wrong. Both I and the courts have recognized that someone can make a mature decision to reject the US and take another citizenship.
Obama COULD have, but he could not be compelled to do so - and he didn’t. That left him a natural born citizen. ANYONE can give up their citizenship anywhere.
At the time that he claimed Israeli citizenship - he was already wanted as an American citizen under a fugitive warrant. He had never previously claimed or applied for Israeli citizenship, never been to Israel, never claimed to be anything but an American - until he brutally murdered another United States citizen ...