“Tradition!” rings out the opening line of “Fiddler on the Roof,” the Broadway play that brought Jewish life to stages around the world. The 1964 musical gives audiences a window into Yiddish-speaking, rural Jewish life in 19th-century Europe. For many people, this image represents Jewish history as a whole. When most Americans think of Jews, they think of Ashkenazi Jews: a term that refers to people of eastern and northern European Jewish culture. In American culture, Ashkenazi Jews are represented by cultural icons ranging from Tevye the dairyman and Yente the matchmaker in “Fiddler” to comedians Woody Allen and Sarah...