You just made my point for me. I don't have a problem with people with dual citizenship under normal circumstances, only when it comes to U.S. security. The U.S. is first and last for me. Let me put this hypothetical case to you: Let's pretend that you're just a regular non-military person and you found, or somehow accidentally stumbled upon, a briefcase full of documents marked "US GOVERNMENT TOP SECRET", and let's say you look at one or two of the documents, and in them, you find information that would be vital to Israeli security (such as, the U.S. has knowledge that a high-level Israeli military official is selling secrets to the Palestinians--something that would be really mind-boggling, but let's pretend just for the sake of argument). A US government official tracks down the briefcase and retrieves it from you and you are told not to reveal to anyone anything you may have seen in the briefcase, as it is top secret information belonging to the U.S. government.
So, what do you do? The information belongs to the U.S., and you have no idea what they are going to do with it. As a loyal American, it would be your duty not to reveal U.S. top secret information to any country. I have no problem with it, since I have allegiance to no other country but the U.S. I would keep my mouth shut. You, on the other hand, would be in a quandary. So, it would be interesting to know how you solved that quandary.
Nevertheless, as you stated the case, it buttresses my view. Any such dilemma would not change because a person is a dual national.
Use the same story but the one finding the information is a Boston born Irish Catholic supporter of the Republican cause and the information is that the British are about to assassinate the entire IRA leadership.