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Unless you're an actual neo Nazi, Jews have been accepted into the whiteness construct since the Holocaust. Arabs not so much...

Many/most people in Israel have some or a large amount of European ancestry, and are generally considered white. This is probably especially true for American ones. Meanwhile Lebanese people do not really have any large connection to European ancestry.

Jews go into the "white" bucket for ethnicity while Muslims go into the "brown" bucket. Anecdotally in America at least this seems true of their general skin color. I'd say a large part is also that America hasn't really valued any middleast Muslim lives since 9/11 (perhaps earlier but I'm not that old).

I don't think I know anyone who would consider an "Israeli-American" to be white, or even any whiter than "Lebanese-American", and I'm solidly Midwestern.

I kind of want to send out a bunch of messages to people asking if they consider one "white" or "whiter" than the other...

I know plenty of people who will give Israel carte Blanche simply because it "needs to exist for Jesus to come back" though, so answers wouod be skewed I imagine.

Sorry I didn't really answer your question, I'm interested to hear other people's takes as well.

Race in general is a social construct that changes to suite racists, like when Italians weren't considered white but now are. But, racists of today consider Israeli/Jewish people with white while Lebanese/Muslim people are non-white/brown.