Not after their agreement in Gal. 2:7-9.
At which point, the terms "the circumcision" and "the uncircumcision" now carried a meaning that at times differed as to whom it was referring to.
Just before Paul was saved in Acts 9, he, along with his unbelieving nation: Israel, was concluded UNcircumcision at the end of Acts 7.
Acts 7:51 Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers did, so do ye. 7:52 Which of the prophets have not your fathers persecuted? and they have slain them which shewed before of the coming of the Just One; of whom ye have been now the betrayers and murderers: 7:53 Who have received the law by the disposition of angels, and have not kept it. 7:54 When they heard these things, they were cut to the heart, and they gnashed on him with their teeth.
Both Jew and Gentile were now "under sin" Romans 1:18-3:20.
Both were now UNcircumcision.
In need of Paul's "gospel of the UNcircumcision."
Romans 2:25 For circumcision verily profiteth, if thou keep the law: but if thou be a breaker of the law, thy circumcision is made uncircumcision.
Romans 3:9 What then? are we better than they? No, in no wise: for we have before proved both Jews and Gentiles, that they are all under sin; 3:10 As it is written, There is none righteous, no, not one: 3:11 There is none that understandeth, there is none that seeketh after God.
While "the circumcision" that "James, Cephas, and John agreed" with Paul in Gal. 2:7-9 that they would now confine their own ministry to referred to "they of the circumcision which believed" Acts 10:45, which is who James, Cephas, and John are writing to in their Epistles.