Racism is about the groups people are placed in by societal perceptions, in which looks are a major but not the sole factor.

Sure, and everyone besides hard core white supremacists considers Ashkenazim to be white. I've hung out with plenty of blatant racists who treated me, as a Jew, as part of their in-group.

Which is not to say that Ashkenazi Jews are not typically considered "white" in mainstream American culture.