You'll find Jewish people who describe it as a racial thing, a religious thing and a cultural thing. Or any of the above.
Admittedly, the racial thing is complicated, as it always is for racial claims. That's because it's hard to keep your genes exclusive. And sometimes, as with Palestinians and Jews (last I heard), the genes are indistinguishable and both semitic. But certainly, geneticists can identify characteristics in people's genes which allow them to identify their semitic ancestry.
My own family has Jewish overlaps. German Jews who escaped Nazi Germany in the 1930s, who are not Jewish by religion but are by ancestry. Ashkenazi Jews, who have a cultural affinity with Judaism, but nothing more. It isn't just a religion thing.
I take your point that in some (although not all) versions of the religion, you can convert and become Jewish. But the pride in ancestry and culture, and of course the country of Israel, is also there. You can't quite have that in the same way without also having Jewish heritage.
So Goldberg made a mistake to exclude race as an element of being Jewish. Even if the definition of race has fuzzy edges (as pretty much all definitions do).
By the way, as far as I know I am not Jewish myself by any definition. But I usually celebrate Christmas with the racially (but not religiously) Jewish parts of my family, although not this year.
Merry Christmas, clo.