Race IS real. And Jews are not a race...arbitrarily defined that is.
That's because we reserve that word for only the several larger groups of peoples in the world who are united by virtue of their geographical descent in the human family tree. Genetic variation is NOT homogeneously spread. There are extended tribes and we call them races and you can identify them by analyzing their genotypes. All the social science political correctness in the world is not going to change that fact.
On the other hand, if I showed you a closely related and extended family of Amish or Presbyterians or Jews or anyone else and argued that they were a tribe, or a race, I would have a point. There are numerous genetic groups with a much greater extent of genetic homogeneity than the population as a whole. So, the common racial definitions are both real and, of course, arbitrary. Observers choose to have cut-off points that don't really exist. That's clear when you see the children of mixed marriages. But just becasue you can mix orange juice and apple juice, doesn't mean they don't exist!