Are the Jews Israel, or is the church Israel? Or does it depend on the context of the passage?

[keras]

That is how I know the Israel of God in Galatians 6:16 is not us

Not right.
The Israel of God in the New Testament:
God’s work with and the development of His people, all faithful Israelites in the Old Testament is continued in the New Testament. Those who presumed that ancestry gave them privileges were chastened. John the Baptist’s strong language indicates how seriously God viewed their pride and arrogance.
John said to the crowds coming out to be baptized by him, "You brood of vipers! Who warned you to flee from the coming wrath? Produce fruit in keeping with repentance. And do not begin to say to yourselves, `We have Abraham as our father.' For I tell you that out of these stones God can raise up children for Abraham. The axe is already at the root of the trees, and every tree that does not produce good fruit will be cut down and thrown into the fire. Luke 3:7-9

Jesus gives a similar warning to those who were trying to trap him: Abraham is our father, they answered. “If you were Abraham’s children,” said Jesus, “then you would do the things Abraham did”. John 8:39 Jesus goes even further in Matthew 8 when he praises the faith of a Gentile Roman Centurion: I tell you the truth, I have not found anyone in Israel with such great faith. Matthew 8:10

Jesus then goes on to make a prediction: I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. But those who were born to the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth. Matthew 8:11-12
Here Jesus is warning his Jewish hearers that unless they recognize him as their Messiah they will be excluded from the Kingdom.

This is how we are to understand Paul when he specifically uses the expression: Israel of God in Galatians 6:16. Peace and mercy to all who follow this rule, even to the Israel of God. Galatians 6:16 For those who hold to a rapture to heaven, they have to think Paul is referring to Jews, or at least Christian Jews, but this simply refutes everything he has said in the first five chapters of this letter.

In Galatians 3:23-29, Paul says we are saved by God’s grace and justified by faith alone in Jesus Christ. Paul is emphatic - people are not saved by ethnicity , by circumcision, by offering animal sacrifices or by keeping the Law of Moses.

In Galatians 4:21-31, those who follow Jesus, are likened to the free children of Sarah. Those seeking to be justified by the Law have been alienated from Jesus and are likened to the children of Hagar. Quoting Genesis 21, they will, he warns: never share in the inheritance…. Paul speaks of our freedom in Christ and our new life in the Holy Spirit. He contrasts living by the Spirit with living by our sinful nature.

See what Paul is saying? We have a choice – grace or law, faith or works? When Paul writes: Peace and mercy to all who follow this rule, [and or even] to the Israel of God, he is obviously referring to all the followers of Jesus who have rejected the legalists who wanted to impose circumcision and the keeping of the Torah Law.

John Stott provides one of the best explanations of this verse: ‘All who walk by this rule’ and ‘the Israel of God’ are not two groups, but one. The connecting particle: ‘kai’ should be translated ‘even’, not ‘and’, or be omitted, as in the RSV. The Christian church has a direct continuity with God’s people in the Old Testament. Those who are Christians today are the true circumcision - Phil. 3:3, ‘Abraham’s offspring’ Galatians 3:29 and ‘the Israel of God’.

And don’t worry about the phrase ‘walk by this rule’ either. The Greek word ‘rule’ is kanon and simply describes a carpenter’s or surveyor’s plumb line. John Stott says, This is the ‘canon’ of Scripture, the doctrine of the apostles, and especially in the context of Galatians 6 the cross of Christ and the new creation. Such is the rule by which the church must walk and continuously judge and reform itself.

In the closing sentences of this letter, Paul is quoting an ancient prayer he would have prayed all his life on the Sabbath. Known as the additional 19th benediction to the 18 benedictions, and based on the Aaronic blessing of Numbers 6:24-26, God is asked in the final prayer for ‘Peace… and mercy on us and all Israel: your people.’ Now Paul prays this blessing on the Jewish and Gentile Christian believers in Jesus for they are the ‘Israelites of God’.

 

[Guojing]

Not right.
The Israel of God in the New Testament:
God’s work with and the development of His people, all faithful Israelites in the Old Testament is continued in the New Testament. Those who presumed that ancestry gave them privileges were chastened. John the Baptist’s strong language indicates how seriously God viewed their pride and arrogance.
John said to the crowds coming out to be baptized by him, "You brood of vipers! Who warned you to flee from the coming wrath? Produce fruit in keeping with repentance. And do not begin to say to yourselves, `We have Abraham as our father.' For I tell you that out of these stones God can raise up children for Abraham. The axe is already at the root of the trees, and every tree that does not produce good fruit will be cut down and thrown into the fire. Luke 3:7-9

Jesus gives a similar warning to those who were trying to trap him: Abraham is our father, they answered. “If you were Abraham’s children,” said Jesus, “then you would do the things Abraham did”. John 8:39 Jesus goes even further in Matthew 8 when he praises the faith of a Gentile Roman Centurion: I tell you the truth, I have not found anyone in Israel with such great faith. Matthew 8:10

Jesus then goes on to make a prediction: I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. But those who were born to the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth. Matthew 8:11-12
Here Jesus is warning his Jewish hearers that unless they recognize him as their Messiah they will be excluded from the Kingdom.

This is how we are to understand Paul when he specifically uses the expression: Israel of God in Galatians 6:16. Peace and mercy to all who follow this rule, even to the Israel of God. Galatians 6:16 For those who hold to a rapture to heaven, they have to think Paul is referring to Jews, or at least Christian Jews, but this simply refutes everything he has said in the first five chapters of this letter.

In Galatians 3:23-29, Paul says we are saved by God’s grace and justified by faith alone in Jesus Christ. Paul is emphatic - people are not saved by ethnicity , by circumcision, by offering animal sacrifices or by keeping the Law of Moses.

In Galatians 4:21-31, those who follow Jesus, are likened to the free children of Sarah. Those seeking to be justified by the Law have been alienated from Jesus and are likened to the children of Hagar. Quoting Genesis 21, they will, he warns: never share in the inheritance…. Paul speaks of our freedom in Christ and our new life in the Holy Spirit. He contrasts living by the Spirit with living by our sinful nature.

See what Paul is saying? We have a choice – grace or law, faith or works? When Paul writes: Peace and mercy to all who follow this rule, [and or even] to the Israel of God, he is obviously referring to all the followers of Jesus who have rejected the legalists who wanted to impose circumcision and the keeping of the Torah Law.

John Stott provides one of the best explanations of this verse: ‘All who walk by this rule’ and ‘the Israel of God’ are not two groups, but one. The connecting particle: ‘kai’ should be translated ‘even’, not ‘and’, or be omitted, as in the RSV. The Christian church has a direct continuity with God’s people in the Old Testament. Those who are Christians today are the true circumcision - Phil. 3:3, ‘Abraham’s offspring’ Galatians 3:29 and ‘the Israel of God’.

And don’t worry about the phrase ‘walk by this rule’ either. The Greek word ‘rule’ is kanon and simply describes a carpenter’s or surveyor’s plumb line. John Stott says, This is the ‘canon’ of Scripture, the doctrine of the apostles, and especially in the context of Galatians 6 the cross of Christ and the new creation. Such is the rule by which the church must walk and continuously judge and reform itself.

In the closing sentences of this letter, Paul is quoting an ancient prayer he would have prayed all his life on the Sabbath. Known as the additional 19th benediction to the 18 benedictions, and based on the Aaronic blessing of Numbers 6:24-26, God is asked in the final prayer for ‘Peace… and mercy on us and all Israel: your people.’ Now Paul prays this blessing on the Jewish and Gentile Christian believers in Jesus for they are the ‘Israelites of God’.

You ignored the premises leading to the conclusion.

 

[keras]

You ignored the premises leading to the conclusion.

The conclusion is indisputable: There is only one people of God - those who follow the Way of Jesus and all the peoples who don't.
You want Jewish Israel to have special treatment? Jesus tells us what that will be; Matthew 8:12

 

[sovereigngrace]

Galatians was written before Paul's final visit to Jerusalem in Acts 21.

If the Israel of God, is us, and he taught us that we are dead to circumcision (Galatians 5:2), then what James and the elders accused him of in Acts 21:18-25 would have been correct.

That is how I know the Israel of God in Galatians 6:16 is not us

How about addressing the biblical evidence above instead of merely expressing your bias and faulty opinions.