On the question titled "Was Abraham Jewish?", the person asked about the jews being of the tribes of Benjamin and Judah and the 10 Northern tribes being called Israel, and you kind of skirted the answer. Were not the 10 Northern Tribes non Jewish Israelites and isn’t it also true that the word Yehudim is only mentioned once in all of the Tanach and the siddur, that being in the Megillat Ester.

All twelve tribes were Jewish. The term "Jewish" as used today does not mean - "descended from the tribe of Judah" (after all converts to Judaism are also Jewish), but rather someone who is descended form the Children of Israel who accepted the Torah at Sinai or those who joined those descendants through the process of conversion set down in the Torah. The term "Yehudi" is referred to throughout the Nach (not only in Megillat Esther) -see for example Zecharia 8:22 where the meaning, according to the sages, is all of Israel- since the king will be from the tribe of Judah. The talmud teaches that Mordecai in Megillat Esther is called "Yehudi" even though he was a descendant of Binyamin, because he was loyal to the unity of G-d.