Donald himself: no conversion and no Jewish parentage so that's a pretty strong "no." Ivana's a more interesting case: Jewish father but non-Jewish mother means halakhically not Jewish. (In Judaism, tribal affiliation is through the dad but Israelite/"Jewish" status generally is traced matrilineally.) And her kids would be even more removed, halakhically. But I suspect she'd be more socially connected to Judaism, and it's probably coincidence Ivanka converted to Judaism and chose to marry a Jew.
(Is Ivanka Jewish? Well, she converted, so if you accept the conversion, definitely. But there's been a bit of a dust-up with some of the more orthodox religious authorities in Israel questioning if the rabbi who oversaw her conversion was stringent enough. The Israeli hyper-orthodox set can be... well, hyper-orthodox. Jewish identity can get complicated. But for most folks, she's squarely in the fold.)
But that's halakha. I've always found the "Jewish enough for Hitler" test more useful. In Nazi Germany they counted you Jewish if you had three or four Jewish grandparents, mischling second class if you just had one and either mischling first class or full Jewish if you had two grandparents. The test gets a bit complicated here, but basically if you were identifying with the Jewish community (if you were registered as a member of a synagogue rather than a church, if you sent the kids to a Jewish school, if the parents were still married, that kind of thing) you were classified as Jewish and if not you got the label "mischling first degree." Which meant you had all kinds of restrictions on you, you probably couldn't work in universities or hospitals or be an officer in the army, but in Germany you didn't get sent to the camps. They were more sweeping outside of Germany - I know in some areas even one Jewish grandparent meant you were counted as full Jewish.
So, Ivanka. Assuming her dad was full Jewish, two Jewish grandparents, she'd at a minimum be subject to all those anti-Jewish laws, possibly face he camps depending on how Jewish their lifestyle was. Even Ivanka, with just the one Jewish grandparent, would face some repercussions. And I understand the law is not to be lightly set aside, that there's a danger in letting oppressors identify a group. But I've always thought if you were Jewish enough to "count" in such a culture-defining trauma (at least among white Jews), if you have some kind of connection with the people that's actually playing out in your life, that's enough for me. I'm all for a more inclusive conception of Judaism, and if Jew-"ish" feels like a better step than Jewish, that's the person's choice but it doesn't make the connection less real.
Actually #1 - and politically this makes me cringe - if you're married to someone who's culturally Jewish, if your daughter's converting and marrying a more clearcut Jew and taking Saturdays off, that's enough for me. Not that Trump probably wants to emphasize it, and not that this makes him at all a good Jew, but I'm not sure I can say Donald Trump has no Jewish (or Jew-ish) identity.
And wouldn't the Breitbart crowd just love that. :^P
Actually #2 - ths one has nothing to do with Trump - when you adopt someone, it irks me a bit that if they aren't Jewish through their birth family they typically have to convert. Birth parents are real parents, and I definitely think that welcoming them into the family is welcoming them into the covenant, that they're situated that way as much as a born child would be.
This got long, I know! It's just fascinating to me, how race and ethnic identity works. I mean Barack Obama was almost universally considered black (outside the black community, at least) even though he only had one black parent and even that man didn't have the typical African-American (slavery - Jim Crow - etc.) family experience as the majority of Afr-Am voters do. Whereas Judaism is a lot more particular, at least in the one sense.
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