Easy. Jeez. You can't even ask a question around here nowadays. It's a hypothetical.
I don't think a person born of two foreigners on US soil would have the right to run for President. I think that is pretty clear. I think it gets more blurred once those two parents are both naturalized before the child's birth. The two people are the same genetically. The only difference is they have now taken the citizenship test, met the requirements for citizenship and sworn loyalty to the USA, been awarded citizenship by the relevent bureaucracy that does that. If I am not mistaken, their child would be completely legal to run for president because the child would be born of two American citizens on American soil (even though those two citizens were actually born in another country).
Where I'm digging at here is- lets say in this instance where the child is technically legal the parents have always taken the child back to the 'home country' once a year to visit relatives and experience his 'native culture'. I would present to you that there would be more questions of that child's actual loyalty because of its active immersion into the other culture than with my example of a child with an unknown father (who is actually a foreigner).
So, the legal technicality does not protect the country in that instance. The child would be completely legal but less loyal than a somewhat less legal child whose loyalty had no such questions.
Right: ‘look, a charging, angry bear ... and by the way I own a teddy bear but it doesn’t look anything like the live bear who is about to ...’