Hear how I rule. Of course not. They are Natural Born American Citizens who are being given the choice to accept the OFFER of citizenship from another country. It is a choice they need not accept, and since their parents were not Israeli ciizens, but American citizens at the time of their birth, they are Natural Born Citizens with an unexercised option that every American has: i.e., to leave. And like every Naural Born American Citizen, it they might even be able to come back and run for office.
The more interesting question is, since they do not have to renounce American Citizenship, would they be eligible to run if they accepted it and didn't leave?
Example 14,998 from the book, "Tough Cases." Get me The Dentist!
Here's the problem we face when discussing the meaning of natural born citizen(NBC) in this particular context. Many people, apparently, wish to evaluate a US citizen's eligibility to be viewed as an NBC, by some application of foreign statutory law. Why would we do that, ever?
To take the argument to the absurd extreme, what would keep one of our enemies, like Korea or Iran or even Russia, from extending - by statute - citizenship to anyone with Iranian/North Korean/Russian blood, irrespective of how many generations that person could actually be removed from those countries. Using the same logic that many apparently wish to apply to Kenya or British or Indonesian law, anyone who was of even negligible of Iranian or North Korean ancestry, would be foreclosed as an NBC precisely because they would now - by statute - be North Korean or Iranian ancestry. Now, does that make logical sense?