Anyone who has ever had Israeli citizenship (by birth, etc) must enter- but most particularly-leave Israel using an Israeli passport.
You are correct, loyalty should be, and was, the sole criteria for clearances. This article refers to new rules which the others didnt.
You and the others might enjoy reviewing a few of the cases involving security clearances. You will note, in the past, clearance was withheld when an individual acts in such a way as to indicate a preference for a foreign country over the United States. Yes, the EXERCISE (voting, use of passport, military service etc) of dual citizenship could be an issue. If you read the decisions, you will note that in the case of Israeli dual citizenship, use of the passport is not an issue, since it is required of Israeli citizens to enter or leave Israel, and military service is generally not an issue for the same reasons. And among the mitigating circumstances that would allow the granting of clearance, dual citizenship is based solely on parents' citizenship or birth in a foreign country, exactly the circumstances we are discussing.