Israel has barred its own citizens from leaving the country, so I wonder where that leaves dual citizenship settlers. Even if they show up at the border with their US passports, I’m sure the border field office computers will out them as an Israelis.
[Israeli Transportation Minister Miri Regev] clarified that only non-Israeli nationals—such as diplomats and tourists—are currently permitted to leave the country.
Edit to add: This is all I’ve found so far, from a law firm. It’s a bit vague, but seems to imply that dual citizenship won’t save you.
In practice, this means that any Israeli citizen seeking to leave the country must now prove that their travel is essential and urgent. Travel for leisure, non-critical business, or personal convenience will not suffice.
In contrast, foreign nationals and tourists holding non-Israeli passports (not including Israeli dual nationals) are not required to obtain special approval.