Defining who is a jew

Who came up with the idea that a Jew is jewish, permanently, because of his mother’s religion and why?

ב"ה Shalom Being Jewish is not just accepting the Jewish religion, it means being born into the Jewish nation, either by lineage of the mother or by conversion which upon, the convert becomes reborn as part of the Jewish nation. As the Talmud put it " A person who becomes a "ger"= a convert it is as if the person was reborn. (Talmud Yebamot 22A) The source that the lineage of the mother is what determines if the born child is Jewish, is in the Mishna In Tractate Kiddushin 66B, which states that the child of a non-Jewish mother is like the mother, whether the father was Jewish or not. The Talmud in Tractate Kiddushin 68b then expounds upon the Mishna and then derives this law from a verse in the Torah that the child born of a Jewish mother is considered Jewish but a child born (from a Jewish father) but a child from a non-Jewish mother is considered non- Jewish. That is to say basically, that it is G-d's idea that only a person born of a Jewish mother is considered Jewish. Why this is so is explained by the Ramban (Nachmanides ) that a child born in the womb of a Jewish woman is like the child immersed in a ritual bath of purity, which then imbued the child with Jewishness. This is codified in the Shulchan Aruch Even Haezer 8:5 and has been the Jewish tradition since the giving of the Torah at Mt. Sinai and according to the Ramban since the time of our forefather Abraham. All the best