jewishness is complicated.
diaspora, mixing, shit, having to hide in hostile cultures meaning having to pass as non-jewish, basically. so...it would be easy to say jewish is non-white as a rule. but then what is whiteness? if you ask 300 years ago...it wasn't anyone with a rosy pink to pale off-white skin. Then there's the whole spending a thousand years in Europe thing for a large portion of social/familial tradition jews. While other traditional hebraic people went in the direction of Asia and Africa and they are decidedly not white.
So the answer becomes yes and no, based on what whiteness was and is. And what jewishness was and is today.
edit: Israel of the past...land of brown people, akkadian, semetic, afro-indus-asiatic. they certainly wouldn't consider themselves 'middle eastern'...relative to Europe in the West.
Israel of today, political frankenstein of war refugees, massacre survivors, and a historically hounded peoples claiming the ancient suppressed Jewish tradition and homeland. The hardened result of mankind's evil and intolerance basically.