A Jewish friend of mine once told me to pay attention to instances where they were classified as white or not and, dang, was she right. She called it being _selectively_ white. I think this is a good example of that.
Asians get the same treatment, though. They're the minority that gets forgotten about, because it doesn't fit some convenient narrative of e.g. "White males are dominating STEM fields", or "Minorities are discriminated against and thus fail to achieve success and affirmation".
They were treated as a separate group throughout most of Europe's history, and faced extreme prejudice and suffering because of it. Hardly seems fair to dilute their achievements and experience by lumping them under 'white'.
For me (a Hispanic) it's odd to see any race categorization at all, it seems like an obsession for both right and left wings in the US. Why does it matter so much? White and Hispanic is not mutually exclusive in a lot of cases, the same for Black and Hispanic or Native American and Hispanic, in most cases it's difficult to even set a race tag.
Race used by statistics and government is of course a simplification, so if you have to do it, you kinda need to embrace the simplicity of it.
Personally I think the term caucasian works well.
Jewish has of course a historic racial component, but practically (again, the simplicity) is more like an identity such as "hispanic". So if you are white hispanic, you're white. If you are jewish, you are white. If you're a black hispanic, you tick the box for black.
Most of the Ashkenazi Jews are certainly white, as in they have white skin. I’d say that even the Sephardic Jews would be considered white based on their skin color alone. But categorizing people by skin color is one of the stupidest things ever, though, as I for myself am white (as in I have white skin) while my brother is more brownish, the reason for that being that our father is white-skinned while our mother is more dark-skinned.