Paul says in Philippians 3:5 that he was “of the people of Israel”, or “posterity of Israel”. The word “people” means genetics. He was pure Jew. Notice he goes further and qualifies his Jewish roots by saying people of Israel. This means he was a true believer in what God promised the decedents of Abraham, Isaac, and Jacob (Israel). He took the promises literally. There were many Jews in Palestine that didn’t. Some had sold out to Rome, Hellenistic culture, or secularism. They were not true Israel (Romans 9:6-8). If posterity did matter, it would doom the Gentiles. They could never be Jewish children of the flesh. They could convert and receive limited covenant blessings (just try entering the Temple), but never be fully Jewish. Paul encourages the church in Philippi, and all Gentiles, by saying genetics plays no part in your standing before God. He favors no race. Faith in the Lord Jesus Christ is what saves. For now that means adoption and equal standing for all people in the true church. In the future it will mean a literal fulfillment of the promises made to Israel with all children of the promise enjoying their inheritance.