Jindal...born here of immigrant parents.
He is a citizen but not a natural born citizen.
Most folks, including most judges, would disagree with you. But your way of thinking is the way it should be!
When growing up, a person is, obviously, very influenced by his parents. If those parents are foreign-born, they will naturally have some loyalty to the old country.
Somewhat divided loyalties, nothing very wrong with that, in general. But it's not something you'd want a potential President to be exposed to.