The provision is, that ‘all persons born in the United States, and subject to the jurisdiction thereof, are citizens.’ That means ‘subject to the complete jurisdiction thereof.’ What do we mean by ‘complete jurisdiction thereof?’ Not owing allegiance to anybody else. That is what it means.
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You do know that means thousand of Jews would lose their citizenship. As they are citizens of both the US and Israel. And as you said, if they owe allegiance to anybody else, they aren't eligible for birthright citizenship.