Paul used the term "my gospel" to differentiate his teachings from the teachings of the Jerusalem church. The Jerusalem church demanded that Greek/Gentile converts be subject to the Mosaic Law. The "circumcision" were those Jews in the church who made that demand.
The Body of Christ includes all who have been saved by putting their faith in the finished work of Christ. Jews had to turn from their being under the authority of Moses and the Mosaic Law and commit to being under the authority of Christ. Many of the Gentiles were involved in pagan religions and they needed to turn away from such things and turn to Christ for salvation and reconciliation. All of mankind needed reconciliation. There's a lot of bad teaching that I have known and seen as far back as I can remember and that is the teaching that the Old Testament and the New Testament are separate testaments and not related. Thus we have this false idea that Jews are forever Jews and Gentiles are forever Gentiles because there are two Gospels - or two means of salvation - with one plan of salvation for Jews and another plan for the Greeks/Gentiles.
There is one Body. Jesus Christ is the promised offspring of Abraham and those who have put their faith in Him have become joint heirs with Him.
Gal 3:16 Now the promises were made to Abraham and to his offspring. It does not say, "And to offsprings," referring to many, but referring to one, "And to your offspring," who is Christ.
Gal 3:28 There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus.
Gal 3:29 And if you are Christ's, then you are Abraham's offspring, heirs according to promise.
Rom 8:16 The Spirit himself bears witness with our spirit that we are children of God,
Rom 8:17 and if children, then heirs—heirs of God and fellow heirs with Christ, provided we suffer with him in order that we may also be glorified with him.
Rom 10:11 For the Scripture says, "Everyone who believes in him will not be put to shame."
Rom 10:12 For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him.
Rom 10:13 For "everyone who calls on the name of the Lord will be saved."