Race has no bright lines in nature. The lefties are right about that one. Unlike them, I don't think that disproves the significance of race entirely.

European Jews share a lot with their non-Jewish co-habitators.

Quite broadly, there's only a few giant categories: Caucasian, Mongoloid, Australoid, Negroid, and what used to be called "Capoid". We can ignore the Africans for a moment, though. If your working definition of white is Caucasian, then yes Jews are and so are Arabs for that matter. You can argue for some mixing that's gone on. And that's when you get into smaller groups like Jews, identifiable from the rest of humanity, but still on this branch.