Good question. There is no consensus on who is considered white. Nazis considered Jews to be a separate and inferior race. At one point in the US, Italians were not considered white. Irish, Greeks and Poles were not considered white at some point, and were discriminated against in the US. “No Irish need apply” (NINA) signs were common at one point in history.

It's not they were considered "not white", that's marxist like thinking dividing amongst visual attributes instead of class.

They were discriminated against because they were considered lesser genetically/socially/etc...

The skin color has little to do with it other than being a phenotype visualizing the genetics that a group hates.

As you pointed out there are plenty of groups (Irish, Italian, etc.) where that phenotype (high melanin) doesn't exist, but the hate and judgement still does...

Ashkenazi Jews are an ethnic group originating in the Near East, but with some admixture from Europeans. At least the plurality if not majority of American Jews are nonreligious, see https://en.wikipedia.org/wiki/American_Jews#Religious_belief...

Originating in Israel/Judea with some admixture from eastern Europe.

Actually thinking about it, probably 'the middle east' since the Jews moved into Israel/Judea from elsewhere at some point.

Definitely considered an Ethnicity.

I think Wikipedia does a decent job of breaking it down: https://en.wikipedia.org/wiki/Jews

There's several Jewish ethnicities. The largest are Ashkenazi (Euro; 90% of American Jewry) and Mizrahi (MENA; majority of Israeli Jewry). Judaism is a religion, so people who aren't ethnically Jewish can convert, but it's also an ethnic identity, so Jews who drop Judaism or convert to another religion (like nearly all famous 19th century Ashkenazim) are still Jewish.