I was born in America, to an American mother, who's father was a career U.S. Air Force pilot (rank: Lt. Colonel at retirement). There is no question then to my status as an American citizen.
But, at the time of my birth, my father was a French citizen. According to French law, like the American law, a child of a French citizen is French. So, I am French. I am not "dual loyal" I am loyal only to America. But, I am a dual citizen. I can't help it. I didn't make the laws. I didn't choose my parents. That's just the way it is.
My father has since been naturalized an American, but that doesn't change the fact that I am a Frenchman according to France. I didn't have to declare any oaths or renounce anything. It is simply a matter of the laws of the USA and France, and has nothing to do with my loyalties.
I don't know exactly how it works, but if the U.S. does recognize your French citizenship, well then, sorry--no security clearance for you.
Under the same circumstances in Israel, at passport control they would make it very unpleasant- even under your facts considering none of minimal contact with France(Israel)- and you would likely miss your flight.