The racing of Jewish people as “white” has a lot to do with developments in American racial politics over the course of the 20th century and little to do with contemporary or historical Jewish people.
In actuality, Jewish people are of West Asian descent and have since absorbed the genes of other human communities on every continent except Antarctica, to the point where we can legitimately be described as transcending the Western social construct of “race” entirely.
By the same token, it should go without saying that assimilated Jewish individuals who identify as “white” should probably learn more about the Jewish community’s historical relationship to, and subjection to discrimination and even violence under, the social regime of “whiteness.”