A citizen at birth is a natural born citizen and has never needed to be naturalized.
You are so wrong. The very fact that application must be made to our consulate in a foreign country to receive a certificate requiring approval by said consul is not a natural act. A natural act is being born in an American hospital where a birth certificate is ROUTINELY issued and no proof is required other than the signature of the attending physician attesting to the actual birth. That is natural! Doing paperwork is not.
In any event, how is it possible to be a natural born citizen in TWO countries simultaneously? Cruz renounced his Canadian citizenship a few years ago.....so was it then that he became a natural born citizen? That last question was sarcasm. What a perfect world we would live in if only people engaged their brain before speaking. Golly, a natural born citizen of two countries!
Read the very first paragraph of this State Department directive: https://travel.state.gov/content/passports/en/abroad/events-and-records/birth.html
It is organic to a nation state to set it's boundaries and decide who is a citizen. The nations do this through the enactment of laws.
In general, Israel's nationality follows jus sanguinis and follows the parents (not the only means of citizenship). In the US, the 14th amendment establishes jus soli as one of the means of citizenship. So how is one naturally born a citizen in two countries? Easy, qualify for both.
For example, a US soldier travels overseas and meets the love of his life a Jewish girl who was born and raised in Israel. They then make a life for themselves in the US and after a few years, the child is born. That child is equally a US citizen and an Israeli citizen. Further, they are an NBC for both countries.
Happens all the time. In fact, one of my Army buds is in this exact situation. He is an NBC of the US, she is an NBC of Israel and until his son turns 18 and decides for himself which citizenship he wishes to renounce, will be a NBC citizen of both countries.