I have seen more than one productions casting fair haired WASPs in these roles. Yes, I know there are blond Jews, but only a small number. And those blond Jews (the real ones--not bottle blonds), well the odd of them singing the "Schmuel Song" about life in a Shtetl are quite low.
I think I must know about 90% of the Jews in New York--and closer to 100% of those in Manhattan. So I am able to tell you about how Jews ought to be represented onstage.
(On the serious side, I know a number of black Jews. A handful of those are members of the same family, and they do indeed use Yiddish words and talk about the ghetto their great grandmother emigrated from.)