I wonder how much it'd shock Eugene if someone pointed it out to him that, in American racial discourse, Irish and Italian folk were once considered "not white." Even Germans were once considered not-white: as recently as WW1, much of the anti-German propaganda up-played the idea that they were somehow more Asiatic than good Anglo-Saxons and Frenchmen.
Before a strong sense of minority ethnicities was forged in the mid-20th century, whiteness was the word applied to the demographic categories that had made it; if they hadn't, they simply wouldn't be considered white. Now we feel it's pretty ridiculous to say that Asians are white, and for good reason. But it's silly for Volokh to pretend that whiteness-as-pale-skin is anything but a pretty recent innovation; in a way, pulling Asians (at least, the successful subgroups, the Chinese and Japanese, and to a lesser extent Koreans) into whiteness is the conservative, traditional approach, and his idea that there's a real "whiteness" that people either do or don't fall into is the kind of ethnic studies navel gazing he'd usually vociferously denounce.