Natural-born citizenship inherently precludes dual citizenship. The Supreme Court affirmed this in Shanks v. Dupont when it said that under the Treaty of 1783, you were either a natural-born subject or a natural-born citizen, including all born in the United States, depending on whether your parents adhered to the crown or whether they adhered to U.S. allegiance. You can’t be both.
You might want to take a look at Afroyim v. Rusk. Afroyim voted in an Israeli election. The State Department tried to take away his citizenship and the Supreme Court rule dc”not so fast, buckos.”
http://en.wikipedia.org/wiki/Afroyim_v._Rusk
And on Obama’s childhood dual-citizenship:
Purpura & Moran v Obama: New Jersey Administrative Law Judge Jeff S. Masin: “No court, federal, state or administrative, has accepted the challengers’ position that Mr. Obama is not a “Natural Born Citizen” due to the acknowledged fact that his father was born in Kenya and was a British citizen by virtue of the then applicable British Nationality Act. Nor has the fact that Obama had, or may have had, DUAL CITIZENSHIP at the time of his birth and thereafter been held to deny him the status of natural born. It is unnecessary to reinvent the wheel here. … The petitioners’ legal position on this issue, however well intentioned, has no merit in law. Thus, accepting for the point of this issue that Mr. Obama was born in Hawaii, he is a ‘natural born Citizen’ regardless of the status of his father.” April 10, 2012
http://www.scribd.com/doc/88936737/2012-04-10-NJ-Purpura-Moran-v-Obama-Initial-Decision-of-ALJ-Masin