To me, this is just a funny little bit of inside-baseball commentary. Following an article in Haaretz called "Jews, White Privilege, and the fight against racism in America," there's been a tug of war going on about whether Jews are, or are not, white. A blogger at the Times of Israel says definitely not. Another blogger who writes at a place called "Jewnited Nations" says that, actually, Ashkenazi Jews are totally white.
This is obviously not my fight, and I don't care about the outcome of the argument. I'm just amused by the fact that they're having an argument over it. Personally, I don't care whether Jews want to think of themselves as white, not-white, white but Jewish first, Jewish and not anything else, or what have you. If they want to be white, I'm fine with that. If they don't, I'm happy to accept their desire to be left out.
It's not an easy question to answer anyway. The word means almost nothing. The underlying concept -- a "white race" or a set of "white races" -- was believed to exist in the 19th century, but now we don't believe there is anything real to which the term refers. In America, we use it very loosely compared to the way it was used a hundred years ago when people thought it meant something important.
In any case, there's probably no better marker for whiteness today than to be concerned about whether you have "white privilege."