Kay Medford originated the role of Mrs. Brice in the Broadway and Hollywood film adaptation of "Funny Girl". Her birth name was Margaret Kathleen Regan or O'Regan. Irish Catholic.
Joan Rivers also spoke out against "Jewface" when discussing the 1993 film version of "The Cemetery Club" starring Ellen Burstyn and Diane Ladd and Olympia Dukakis (Lainie Kazan was the only Jew in the movie). The 1986 movie version of "Brighton Beach Memoirs" cast uber-shiksa Blythe Danner as the strong Jewish mother Kate Jerome and many complained she was miscast.
Italian-American Anne Bancroft played her share of Jewish mothers - but she had an urban ethnic New York sensibility (and was a superb actress).
There is a certain "New York Jewish" thing as well as Jewish humor that are hard to capture if you aren't the authentic real thing and can feel like fake caricature if "acted".
I think Jane Lynch will be good in the part, Jewish or no.