I feel like a lot of people missed your point- not just about Jews but the concept of "white" in general has been nebulous throughout history.

Irish people, Italian, greek... Pretty much all Mediterranean people. There's been tons of conversations about whether Egyptians should be considered white, and which ones. The Nazi's labelled the Japanese as "honorary Aryans".

"White" is not based in anything physical or real. It's a concept made up to exclude others and has changed based on who they want to include or exclude.