Goldberg is not an anti-Semite, but she was confused—and understandably so. In my experience, mistakes like hers often happen because well-meaning people have trouble fitting Jews into their usual boxes. They don’t know how to define Jews, and so they resort to their own frames of reference, like “race” or “religion,” and project them onto the Jewish experience. But Jewish identity doesn’t conform to Western categories, despite centuries of attempts by society to shoehorn it in. This makes sense, because Judaism predates Western categories. It’s not quite a religion, because one can be Jewish regardless of observance or specific belief. (Einstein, for example, was proudly Jewish but not religiously observant.) But it’s also not quite a race, because people can convert in! It’s not merely a culture or an ethnicity, because that leaves out all the religious components. And it’s not simply a nationality, because although Jews do have a homeland and many identify as part of a nation, others do not.
Instead, Judaism is an amalgam of all these things—more like a family (into which one can be adopted) than a sectarian Western faith tradition—and so there’s no great way to classify it in English. A lot of confusion results from attempts to reduce this complexity to something more palatable for contemporary conceptions.