It’s very interesting, how definitions differ and how they are changed; almost every week another definitions. :-)
Ashkenazi means “German Jews” and is a term used for Jews living formerly in Europe/EastEurope; mainly in “Staettele”; mainly speaking “jiddish”. Those jews who left Europe (alija, beginning ~1880) from Russia, Ukraine, Poland, … Long before Hitler 1933.
Ethnically they are not Semites. Israeli Jews immigrated from Europe/Easteurope to Palestine/Israel or USA/Canada are the ashkenazi-part.
Semites = children of “Sem” includes Arabs and jewish Arabs and oriental jews; mizrachim and sephardim are the semite-/oriental-part; its an ethnical group with different religions, including jewish religion.
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Can an atheist be a Jew? If jewish is a religion ==> no.
If a Jew converts to Catholic-religion or converts to Islam, can he/she stay a Jew? If jewish is a religion, answer should be “no”.
I know, for political propaganda reasons (#ZionHasbara), the definition of “jewish” (religion or ethnic-group) is important and is changed regurarly, depending of political goals.
Ben Gurion made a sort of “pregnant vergine”: he claimed zionism is secular, but he used/abused lots of arguments, stories, legends from the Bible.
This is the reason, why President Truman made a correction: https://www.screencast.com/t/riZ9j9nDL9l
Shlomo Sand (see amazon) describes this in two books in detail.