Israel of God (Gal 6:16):

“And as for all who walk by this rule, peace and mercy be upon them, and upon the Israel of God. “ (ESV Gal 6:16)

This term is unique in the Bible. Thus warning bells should immediately go off when someone tries to base doctrine on it.

More significantly, Dr Peter Richardson did a very comprehensive historical study of this term and the associated ‘replacement’ doctrines (see ‘Israel in the Apostolic Church’) and states that  the adoption by Christianity of Jewish prerogatives and attributes, and in particular with its assumption of the name 'Israel' took place over a long period.

In fact, Richardson argues that the equating of the Church as the 'true Israel' does not occur, until the mid-second century in the works of Justin Martyr.

Clearly then, in Paul’s time no-one saw this term as meaning the Christianity was the ‘Israel of God’.

Further though, look at the context. If Paul was referring to these Gentile converts as Israel, it would undermine his effort to persuade them to remain non- Israelites by resisting the offer of proselyte conversion to resolve their identity problems.

Paul emphasizes that God has included them by way of the Messiah into Abraham's family, but he does not declare them to be members of the family of Israel. Rather, it is likely that Paul is reflecting a sentiment not unlike that expressed in Romans 11 toward his fellow ‘natural’ Israelites, looking for a day when there will be peace among them, rather than division.

While the whole Galatians epistle focuses on the circumcision/proselyte issue, at this point in Gal 6, Paul is not seeking to represent the fate of some of Israel, but to warn the wild olive (the gentiles) of the fate it/they will meet, if it/they are unfaithful. An allegory intended to condemn Gentile arrogance can’t suddenly become a source for descriptions of Jewish exclusion and replacement.

Rather, in the context that the Apostle Paul sees the coming restoration of all through the Messiah’s appearance and the prophetic inclusion of Gentiles in the Kingdom, it may well be that Paul is in some ways reflecting on Ps 126 which foresees a time when all Israel will be properly and truly called the ‘Israel of God’.