Are they Israelis?Americans? Jews just like the other Jews around them? None of the above? All of the above? Once they've got the answers, what about their kids?
Apparently it's complicated, just like real life. So Udi Sommer - one of them himself - set out to see what answers were on offer. According to this article, his investigations haven't given him much of an answer. It seems, however, that he's focusing on Sabras who move to the US, not on American Jews who moved back and forth - that's probably yet again a whole different issue.