I would disagree with your statement that "Jew is not a race." Many Jews (IME) marry Jews, because it's easier to marry someone in the same culture as you. Additionally, you know how there are some medical conditions that one race is more prone to/is exclusive to a race (sickle cell anemia comes to mind)? Ashkenazi Jews are more prone to Tay-Sachs Disease than other ethnicities. Also, there are foods, phrases, and a language that's known to be Jewish- similarly, there are aspects of Hispanic, African American or Native American races that are exclusive to their race
, not their beliefs.