"Whiteness" is a meaningless, Anglosphere concept. Ashkenazi Jews are beyond essentialist Anglosphere crap.
As an aside, "Europe" and the "Middle East" aren't meaningful genetic labels. Divisions between "Europe" and the "Middle East" genetically are the WEAKEST on Earth. No human group has been reproductively separate from another so "race" isn't a thing; "Europeans" and "Middle Easterners" in particular share deep direct ancestry and similarities between the two are because of that and not due to "convergent evolution". This means that if "race" were a biologically meaningful concept, there would be no separation between "Europeans" and the "Middle East". There's also that pesky thing called genetic drift, but I guess you're not educated on that.
Second aside, what does one mean by "European"? You can't meaningfully tell anyone who has basic knowledge of genetic relationships that any Finn is closer to any Italian population than he would be to an Ashkenazi Jew. Same with Russians vs Ashkenazi Jews vs Italians (All Italian subpopulations are genetically closer to Ashkenazi Jews than Russians).