There are many different varieties of Jew-ish. Some identify with the heritage, some with a belief system, some with a particular brand of God, some with a commitment to the Zionist movement, some with a culture. I think it used to be true that no one was considered an authentic Jew unless their mother had been one. I don’t think there’s such a thing as a genetic Jew. Maybe there is.
Elizabeth Taylor played the Jewess Rebecca in IVANHOE even before she converted to Judaism.
I think, barring the regime of political correctness, a director should be able to cast it based on old films of Fanny Brice and a non-politically-correct acquaintance with the great tradition of « Jewish comedy » (cf., Mel Brooks, Milton Berle, Jack Gilford, Zero Mostel, etc.).
I don’t think the actress need get a blood test or profess any allegiance to the god of the old testament. In my opinion.