We come to the argument which isn't an argument at all.
The covenant with Abraham and his Son Isaac came through the line of Jacob. Jacob was called 'Israel' and all born of the line of Israel are descendants of Isaac and inheritors of the promise of Abrahams as his descendants through Isaac.
The twelve tribes of Israel are the twelve son of Jacob who is called Israel.
“The scepter shall not depart from Judah, nor the ruler’s staff from between his feet, until Shiloh comes; and to him shall be the obedience of the peoples”. (Gen 49:10)
Numbers 24:17:
“I see him, but not now; I behold him, but not near: a star shall come out of Jacob, and a scepter shall rise out of Israel…”
Judah, the chosen tribe from which the Messiah would come. Judah made the royal tribe.
I will ask you a question if a member of the tribe of JUDAH is not circumcised he is still a Jew?
If a member of any tribe is uncircumcised is he still a Jew?
There is a historic line of many events which lead to Judah being Chosen by God as the royal line.
There is the priestly line through Levi but we know the priestly line was Levi and Judah because of the mother of the high priesthood was from the tribe of Judah.
The descendants of Abrahams line is through circumcision and promise.
But more so through the chosen Son who was Isaac. Through any other son you would never have had the Israelites or the tribe of Judah.
I personally believe, we cannot think or assume that anything changes the will or promise of God because of mans own scholarly views. If we read the bible we see nothing is left to mans way of thinking it is simply Gods choice about whom he choses. The choice shows that it is not man who decides.
using your logic that abraham was a jew would make ishmael and all of hagar's and keturah's children jew too.
they aren't considered jewish.