There are three words for the Jewish race: Hebrew, Jew, and Israel. There are three categories of Jews. The racial Jew is anyone with the genes of Abraham, Isaac, and Jacob. The regenerate Jew is any Jew who has accepted by faith the Messiah, Jesus Christ as their Savior. The religious Jew is the non-regenerate Jew who chooses to reject Jesus Christ.
All nations are founded on physical birth except the nation Israel, which was founded on the new birth. For the first three generations, the basis for the nation Israel was founded on regeneration. Abraham was a Chaldean by natural birth. Through regeneration he became a Jew. He “crossed over the river” and became a Hebrew or the first missionary.
Abraham was saved in Ur of the Chaldees as a Gentile. God’s absolute righteousness (+R) was imputed to him upon faith belief and Abraham was then justified by God the Father. Abraham was justified or vindicated in the eyes of the unbeliever when he offered Isaac. James 2:21; Gen. 12:2; Deut. 7:6.
“Was not Abraham our father justified by works when he offered up Isaac his son on the altar?” (James 2:21, NASB)
“And I will make you a great nation, And I will bless you, And make your name great; And so you shall be a blessing;” (Genesis 12:2, NASB)
“"For you are a holy people to the LORD your God; the LORD your God has chosen you to be a people for His own possession out of all the peoples who are on the face of the earth.” (Deuteronomy 7:6, NASB)
In the land of Canaan, Abraham was circumcised, which was the sign that he was now a Jew. Abraham was the pattern for salvation in the Old Testament for both Gentile and Jew as he was both a saved Gentile and a saved Jew.
Abraham had two sons - Ishmael and Isaac. Ishmael (from which comes the Arabic race) was not born-again and remained a Gentile. Isaac was born-again and became a Jew. Isaac had two sons - Esau and Jacob. Esau was not born-again and remained a Gentile. Jacob was born-again and became a Jew. All of Jacob’s sons were racially Jews and formed the new nation of Israel. They were also all believers and therefore regenerate Jews.
The Abrahamic Covenant is based on regeneration, hence the promises made to Abraham and believed by him can only be passed on to another believer - in this case Isaac. Ishmael was the natural seed, but not the spiritual seed of Abraham. Isaac was both natural seed and spiritual seed.
The will of God had not failed the Jews, but the Jews of Paul’s day had failed the will of God by negative volition towards Jesus Christ. Therefore, as natural or racial, but not spiritual seed of Abraham, they could not receive God’s promises made to Abraham.
Physical decent or natural birth is worthless in transmission of divine promises. They can only be transmitted in regeneration. Likewise, Jacob and Esau have the same father and mother, but the difference again is in spiritual birth.
All people born from then on through the Old Testament and beyond were racial Jews, but not necessarily regenerate. The Jewish race from the tribes of Israel on is based on genes, not on regeneration as in the first three generations. This is why the phrase, “God of Abraham, Isaac, and Jacob” is often used. Others have the genes of Abraham, but not the genes of Isaac and Jacob i.e., Arabs. The Jews are a race which does not lose identification and is part of their discipline.