Before the religion of Israel was called Judaism, it was the religion of Israel. Before we had Torah, we had Bnei Israel (Children of Israel). Before we had the 613 mitzvot, we had Am Israel (Nation of Israel). Why, in the Torah, are we called “Israeli,” just like in the Tanach the Arabs are called “Arabi?” It’s because both people are a distinct nation (Israeli is Hebrew for Israelite). Why is there a religion called Judaism? One of the tribes of Israel is called Yehuda (Judah). People of the tribe of Yehuda are Yehudi. By the time we were conquered by the Greeks and Romans, the tribe of Yehuda was the most dominant tribe of Israel. Therefore, instead of being known as Israeli, the world knew us as Yehudi (Judites, Judeans, Jews, etc…). What was the religion of the Judeans? Judaism. Judaism is akin to a religion called Arabism (which there is no such thing anymore). Therefore, one can convert from the religion of the Jews and still remain a Jew. One can be a Jewish Muslim or Jewish Christian. Arabs can also convert to Judaism, and since our laws don’t allow us to distinguish between a convert and a native, that Arab will forever be considered a Jew, even if he converts to Islam.
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from the article: You can't be a Jewish Muslim