Not only does the bible not teach that there are two distinct peoples of God, ethnic Israel and the gentile Church, but it is very explicitly opposed to this idea. John 10:16, John 17:22-23, Ephesians 4:4-6, Colossians 3:11
For one thing, the Church, defined as the group of true believers of God, existed in the Old Testament, long before the outpouring of the Spirit on the Day of Pentecost, Acts 7:38, and furthermore, the clear teaching of the New Testament is that the modern day Church is really just the joining with and the expansion of God’s people that He originally chose.
According to Paul being an true Israelite has never been based on anything other than faith in God, Romans 2:28-29 & 9:6-8 and only those who have been called according to God’s promise are Abraham’s seed by faith. Romans 9:8
Hence, all who have [Christian] faith are Abraham’s children, and are the
true Israelites of God. Galatians 3:26-29
When Paul deals extensively with the whole question of the place of Jews and Gentiles in the people of God, in Romans 11, he shows that there is just one people, symbolized by one good olive tree; unbelieving individual Jews may be broken off of that tree of true Israel and believing individual Christian Gentiles may be grafted in; but there is still one tree, one body, one people of God. Paul teaches elsewhere that there is no difference between Jew and Gentile in Christ, but that all believers are members of the same body, citizens of the one Christian congregation of the Israelites of God and the inheritors of all the promises made to Abraham. Ephesians 2:11-22, 3:6, Galatians 4:26-31, Phil. 3:20, Hebrews 12:22-23
In short, there is and always has been just one people of God, and that people includes all those who are grafted in to God’s “good olive tree” to become Abraham’s children by faith, people from every tribe, race, nation and language, every faithful, born again Christian believer. Revelation 5:9-10, Isaiah 56:1-8, Psalms 73:1