Why do some people believe that people who practice Judaism are a race/ethnicity?

I was told yesterday that I look Jewish. I am Italian/Greek, raised catholic but no longer follow that religion.
Is it because the nazis considered being a jew a race. I've noticed that some jews call themselves a race in order to feel superior to other people.
How come there are black Jews, and jews with blond hair and blue eyes if it is a race?
What about converts, do there genetics change when they go to a synagogue?