As many as desire to make a fair shew in the flesh, they constrain you to be circumcised; only lest they should suffer persecution for the cross of Christ. For neither they themselves who are circumcised keep the law; but desire to have you circumcised, that they may glory in your flesh. But God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world. For in Christ Jesus neither circumcision availeth anything, nor uncircumcision, but a new creature. And as many as walk according to this rule, peace be on them, and mercy, and upon the Israel of God. ~ Galatians 6:12-16

Ellicott’s Commentary for English Readers has the following to say about the phrase the Israel of God.

And upon the Israel of God.—The benediction is addressed, not to two distinct sets of persons (“those who walk by this rule” and “the Israel of God”), but to the same set of persons described in different ways. “And” is therefore equivalent to “namely:” Yea, upon the Israel of God. By the “Israel of God” is here meant the “spiritual Israel;” not converts from Judaism alone, but all who prove their real affinity to Abraham by a faith like Abraham’s.

Now consider the following texts:

Know ye therefore that they which are of faith, the same are the children of Abraham. And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. So then they which be of faith are blessed with faithful Abraham. ~ Galatians 3:7-9

Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, Cursed is everyone that hangeth on a tree: That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith. ~ Galatians 3:13-14

For ye are all the children of God by faith in Christ Jesus. For as many of you as have been baptized into Christ have put on Christ. There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise. ~ Galatians 3:26-29

And he (Abraham) received the sign of circumcision, a seal of the righteousness of the faith which he had yet being uncircumcised: that he might be the father of all them that believe, though they be not circumcised; that righteousness might be imputed unto them also: And the father of circumcision to them who are not of the circumcision only, but who also walk in the steps of that faith of our father Abraham, which he had being yet uncircumcised. ~ Romans 4:11-12

Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed. ~ Romans 9:6-8

Now we, brethren, as Isaac was, are the children of promise. ~ Galatians 4:28 

In scripture, Jesus did not think the religious Jews of his day, those who were determined to oppose him, had any special privilege with God. When they claimed that Abraham was their Father, Jesus said, If you were Abraham’s children, then you would do what Abraham did. As it is, you are looking for a way to kill me, a man who has told you the truth that I heard from God. Abraham did not do such things. You are doing the works of your own father. ~ See John 8:39-41

They responded, We are not illegitimate children, the only Father we have is God himself. Take note that these Jews claimed to be the children of God because of their physical descendancy. To this Jesus replied, If God were your Father, you would love me, for I have come here from God. I have not come on my own; God sent me. Why is my language not clear to you? Because you are unable to hear what I say. You belong to your father, the devil, and you want to carry out your father’s desires. He was a murderer from the beginning, not holding to the truth, for there is no truth in him. When he lies, he speaks his native language, for he is a liar and the father of lies.” ~ see John 8

Notice that Jesus tells these religious Jews who were actual physical descendants of Abraham that they were not Abraham’s true children, and thus they were not God’s children. Jesus says, You belong to your father, the devil. 

In contrast, notice the words of Jesus to Nathanael. “Behold an Israelite indeed, in whom is no guile”! ~ John 1:47

The words of Jesus ought to be enough to convince us that there is something to being a true Israelite in the eyes of God, and simply being born of Israeli/or Jewish descent doesn’t make a person a true Israelite in the eyes of God. A person can be 100% a physical descendant of Abraham, and not be a child of God, because he doesn’t follow the faith of Abraham.  

In his response to the Jews in John 8, Jesus says, And because I tell you the truth, ye believe me not. Which of you convinceth me of sin? And if I say the truth, why do ye not believe me? He that is of God heareth God’s words: ye therefore hear them not, because ye are not of God. ~ John 8:45-47

The children of God are the children of Abraham, and Abraham’s children are the Israel of God. When a Gentile believes the gospel and follows Jesus, he is grafted into the family of Abraham. The Jew is not grafted into a Gentile entity called the church. Rather the Gentile is grafted into a Jewish entity called Israel (Abraham’s family) along with Abraham’s physical descendants who follow Christ. This union of Jews and Gentiles in Christ is the church, and the Israel of God that Paul speaks of in Galatians 6.

It is important to note that in connection with the Israel of God, Paul (a Jew after the flesh) says, But God forbid that I should glory, save in the cross of our Lord Jesus Christ, by whom the world is crucified unto me, and I unto the world. For in Christ Jesus neither circumcision availeth anything, nor uncircumcision, but a new creature. ~ Galatians 6:14-15

In his letter to the Colossians, Paul speaks of being circumcised with the circumcision made without hands. This is a reference to the circumcision that occurs in the heart through faith in Jesus Christ. In Romans 2, Paul rebukes the Jew who boasts in the law, while not keeping the law, and says, For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God. ~ Romans 2:28-29

When the Pharisees and Sadducees came to John the Baptist, John warned them not to boast in their physical descendancy.

But when he saw many of the Pharisees and Sadducees come to his baptism, he said unto them, O generation of vipers, who hath warned you to flee from the wrath to come? Bring forth therefore fruits meet for repentance: And think not to say within yourselves, We have Abraham to our father: for I say unto you, that God is able of these stones to raise up children unto Abraham. ~ Matthew 3:7-9

John the Baptist, a righteous Jew, rebukes those who relied on their physical lineage, rather than having their hearts right with God.

In the book of Acts, the Apostle Paul (a righteous Jew) rebuked a Jewish sorcerer, calling him “thou child of the devil.”

And when they had gone through the isle unto Paphos, they found a certain sorcerer, a false prophet, a Jew whose name was Barjesus: Which was with the deputy of the country, Sergius Paulus, a prudent man; who called for Barnabas and Saul, and desired to hear the word of God. But Elymas the sorcerer (for so is his name by interpretation) withstood them, seeking to turn away the deputy from the faith. Then Saul, (who also is called Paul,) filled with the Holy Ghost, set his eyes on him. And said, O full of all subtilty and all mischief, thou child of the devil, thou enemy of all righteousness, wilt thou not cease to pervert the right ways of the Lord? And now, behold, the hand of the Lord is upon thee, and thou shalt be blind, not seeing the sun for a season. And immediately there fell on him a mist and a darkness; and he went about seeking some to lead him by the hand. Then the deputy, when he saw what was done, believed, being astonished at the doctrine of the Lord. ~ Acts 13:6-12

Later in 1 Thessalonians 2 we read the following from the words of the apostle Paul as well:

For you, brothers and sisters, became imitators of God’s churches in Judea, which are in Christ Jesus: You suffered from your own people the same things those churches suffered from the Jews who killed the Lord Jesus and the prophets and also drove us out. They displease God and are hostile to everyone in their effort to keep us from speaking to the Gentiles so that they may be saved. In this way they always heap up their sins to the limit. The wrath of God has come upon them at last. ~ 1 Thessalonians 2:14-16

Notice that Paul is referring to evil within Jewry. He says of these Jews, (1) the churches suffered from them (2) they killed the Lord Jesus (3) they killed the prophets (4) they drove us out (i.e. they opposed Paul’s ministry). Paul says they displease God, they are hostile to the spreading of the Gospel and because of these things they are heaping up their sins to the limit and the wrath of God has come on them at last.

Though there are many good Jews, and some who trust in Jesus as their Savior, being Jewish doesn’t mean that a person is a child of God. Paul tells us in Romans that not all within Israel (Abraham’s physical descendants) are truly Israel.Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called. That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed. ~ Romans 9:6-8

According to Paul, those who are Abraham’s children according to the flesh only (like those whom Jesus rebuked in John 8) are not the children of God, but the children of the promise (such as Nathanael) are the seed, Among Abraham’s physical descendants, only a remnant are the children of God. This is what Paul is explaining throughout Romans 9, and it is why God said Jacob have I loved, but Esau have I hated. ~ Romans 9:13

God did not have a personally hate for Esau. Esau represented that which was born after the flesh. Esau was the firstborn of Isaac who did not value his birthright but sold it for a bowl of stew. Esau represents those who sell their inheritance to satisfy their flesh. Flesh cannot please God, nor does it desire God, or seek after God.

Jacob, on the other hand, represents those who hunger and thirst for God, for the living God. Both Esau and Jacob were children of Israel, but one was rejected and the other blessed. One did not esteem his birthright, the other was willing to do whatever it took to get it. Esau represents the physical carnal nature that rebels against God. Jacob represents the heart that longs for God.

Esau and Jacob represent the two types of Israelites. There were those who were physical descendants of Abraham but did not have a heart for God, and there were those who were physical descendants of Abraham who had a heart for God. They are the remnant, the true Israel within Israel, and this true Israel within Israel are the children of God and the family of Abraham.

This is why Jesus often taught the crowds saying, “your Father in heaven”. Over and over again, in his sermon on the mount, Jesus referred to God as their Father. He never used such language with the Jews who opposed him and hated him. But to the common people who came to him to be taught, he taught them that their Father loved them.

If I may, I will also add that Jesus never taught the common people that they we God’s enemy and that they were under God’s wrath because of their sin and that they deserved to be punished, etc. Jesus taught them that their Father loved them, and their Father was the God of Abraham.

And ought not this daughter of Abraham, whom Satan had bound, lo, eighteen years, be loosed from this bond on the Sabbath day? ~ Luke 13:16

Jesus divided the true children of Abraham from those who were not within Israel. Those who were and are the true children of God (whose hearts are circumcised) are the family of Abraham, and we who are Gentiles in the flesh have been united with them by being grafted into their family tree! Together Jews and Gentiles in Christ Jesus are the Israel of God!