The New Testament thread of Paul in Romans 2: 28-29, Romans 9: 6-8. Galatians 4:25-26, Galatians 3: 16-29, and Galatians 6: 16 is very important in understanding the transformation of physical Israel into that spiritual house I Peter 2: 5-9 talks about. That part of physical Israel which rejected Jesus Christ is not the spiritual house Peter describes, and is not now the chosen people of God. Read I Peter 2: 5-9.
These texts are contradicted and lost under Christian Zionism which teaches that God now has two separate and different peoples, the church as a Body of Christ and All Israel, meaning all physical Israel, which is still the chosen people based on race. What Paul says is that race as a way of getting into the kingdom of God was done away with and entry is no longer by having the physical bloodline from Abraham, but that the seed, spiritually and physically, from Abraham is Jesus Christ. All who are in Christ are the spiritual seed of Abraham. So then, as Paul says in Romans 2: 28-29 the true Jew is no longer one who can boast of being a descendant from Abraham, but the true Jew is one who is a Jew inwardly, who has a circumcision of the heart and is in the Spirit.
Peter in I Peter 2: 5-9, confirms what Paul was teaching and talks about Christians being a spiritual house, a chosen generation, a royal priesthood, an holy nation, a peculiar people. John, the only Apostle who lived into old age, maybe into his nineties, also supports Paul in verses in the early chapters of the Book of Revelation, especially Revelation 2: 9, "I know the blasphemy of them which say they are Jews, but are not, but are of the synagogue of Satan." This is in agreement with Romans 2; 28-29, and adds that Jews who boast of their physical lineage and their identity as the chosen people blaspheme.
The restoration or really the transformation of physical Israel mired in the physical of racism as the descent from Abraham, circumcision, the literal temple building and all the shadows that point to Christ and the New Covenant begins in II Kings 21: 13, saying that God will stretch the plummet line over Jerusalem, meaning he will judge Israel, and will wipe Jerusalem, or Israel, like wiping a dish clean, and will turn Jerusalem, or old Israel upside down.
Then Isaiah 29: 16 picks up on this idea of turning old Israel upside down and in talking about it being esteemed as the potter's clay, points to Jeremiah 18:1-6, the parable of the potter who makes a pot on his wheel which is marred, and then puts that same lump of clay back on his potter's wheel and makes a new vessel out of the same lump which ios seen as pleasing to the potter who is God. A potter can take a still wet pot he has just thrown on the wheel, mix it with dry powdered clay, put it back on the table and knead it, then put it on the wheel and make an entirely different pot. I have done this when I was a potter.
The Christian Zionists in their claim that physical Israel will all be saved sometime in the future use Amos 9: 11 as a proof text that God will turn again to the Jews to deal with them and save all of them. But they extract that one verse out of the verses from 9: 8-11, saying that God will judge old Israel, such that verse 11 is about the restoration or transformation of Israel in Jesus Christ.
Then the Christian Zionists fail to understand the parable of the vineyard in that important chapter in Luke, Luke 13. In the parable the Father says to cut down the fig tree which is old Israel because it is bearing no fruit. But the Son as the dresser of the vineyard asks the Father to let him dig about and dung it, and if it then bears no fruit to cut it down.
Christ pruned down old Israel in transforming it from a physical house into a spiritual house. In Acts 2: 41 about three thousand Jews were converted into spiritual Israel and in Acts 4: 4 about five thousand believed. But these groups and all who accepted Christ and began to give up their bondage to the shadows of the Old Covenant and give up Talmudic Judaism, the religion of the Pharisees, were a Remnant, the Remnant of Israel. Those of Old Israel who rejected Christ are said to be cut off in Romans 11: 17
Paul's teachings in Romans 2; 28-29, Romans 9: 6-8 and Galatians 3: 16-29, Galatians 4: 25-26 form the background for understanding his cryptic sayings in Romans 11: 26 (and so all Israel shall be saved) and talking about the Israel of God in Galatians 6; 16.
In Romans 11: 16 he is almost making a play on words. Since all who are saved are Israel, that is, all who are saved have their identity in Christ in Israel (because he came to save the lost sheep of the house of Israel), then all Israel shall be saved. Its not a prophecy for a future salvation of all Jews. The traditional Calvinists had some understanding of this.
In Galatians 6: 16 when Paul talks about the Israel of God, what he is doing is pointing out that there is a spiritual Israel called a spiritual house by Peter in I Peter Chapter 2 which is the Israel of God. In accordance with Romans 9: 8, the physical descendants from Abraham who rejected Christ are not the children of God, therefore they are not the Israel of God. What he means is that saved people of any race are the Israel which is of God as opposed to that Israel which is not of God. Those of physical Israel and their surrogates or proxies, the Christian Zionists, do not understand or accept Paul's teachings I have mentioned, especially that Israel was translated into a spiritual house and those who rejected Christ are not part of that house.
Galatians 6: 16 - the phrase "ton Israel tou Theon" - or "the Israel of God," has the Greek article before Israel and tau, or "of", after Israel. Those who know and understand what Paul said in Romans 2: 28-29, Romans 9: 6-8, and Galatians 4: 25-26 recognize that Paul is indicating by the article in front of Israel and "of" God after it, is not using "Israel" in the sense of physical Israel, which he usually means by "Israel." For example, in Romans 11: 7, Paul means by Israel physical Israel, "What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded."
There is still another text by Paul which supports his teachings in Romans and Galatians on the difference between physical Isreael which rejected Christ and the Israel of God. Its Ephesians 2: 11-13, "Wherefore remember, that ye being in time past Gentiles in the flesh, who are called Uncircumcision by that which is called the Circumcision in the flesh made by hands;
12. That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
13. But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ."
This text does not spoon feed those who are followers of the theologies which hold that physical Israel, or All Israel, even now remain the chosen people of God. What Paul is saying, though, is that Gentiles who were once alienated from the commonwealth of Israel became part of Israel through the blood of Christ. The capital C Catholic Church did not replace physical Israel, and the diepsnationalist capital C church, following the Catholics in this, is, as the ekklesia, or meeting, congregation or assembly, not a Body of Christ. Rather, physical Israel was transformed as Jeremiah's parable of the potter (18: 1-6) shows. Israel was changed in Christ, but it is still Israel, and those who call themselves Israel, but who reject Christ are not the Israel of God, but as Revelation 2: 9 says, may blaspheme in claiming to be the Israel of God.
There is one fold in Christ, as John 10: 16 says, not two folds belonging to Christ.