Why the son of Avraam, Ishmael and the son of Issac, Eisav, did not become Jews?
Technically, the forefathers Avraham, Yitzchak and Ya'akov, are not exactly "the Nation of Israel" in the common sense of the word, and accordingly, not all of their children are "members of the tribe". The forefathers are the prototype and the fathers of the people of Israel, yet there are two covenants, that of the forefathers (Breishit 15, 18; Tehilim 105, 9), and that when we left Egypt at Sinai (Shmot 24). The forefathers are like the top of the pyramid or family tree, where technically, they are still individuals (lacking the 2nd covenant), but they knew prophetically that the Chosen People of Israel will soon descend from some (!) of their children, and receive the Torah for the 2nd covenant to become the Nation of Israel (Breishit 15, 13-16). Jacob and his 69 sons went down to Egypt, but his name had already been changed to “Israel” (Breishit 32, 28). ("Jewish" and "Israel" have been synonymous and interchangeable for most of Jewish history, already 2,700 years, since the exile and loss of the 10 tribes which had seceded from Judah/Judea, and subsequently there's no need to differentiate between Judah/Jew and Israel).