The traditional answer to the identity of the opponents of Paul is that they are Jewish Christians that desire to impose the law on Gentile converts – Judaizers. The term appears in the New Testament only in Gal 2:14 (although a form appears in but is found in a number of secular sources (Plutarch, Cicero 7:6; Josephus JW 2.17.10; Ignatius, Magn 10.3) with the basic meaning of “to live as a Jew in accordance with Jewish customs.”
As early as 1831, F. C. Bauer (from the Tübingen school) suggested that there was a split within early Christianity. Based on 1 Corinthians, he understood that there were two major parties, a Peterine party (which included the “Christ party”) and a Pauline party (which included the Apollos party). Those that followed Peter claimed to be “of Christ” since their leadership had been followers of Christ in his earthly ministry, while Paul and Apollos did not know Jesus directly. The Jerusalem Christians were of the Peter division, a party that was unable to counter Paul’s argument for a gentile mission, but were not particularly pleased with it either. The opponents at Galatia were the radical elements of the Peterine division. The serious problem with this view is that it makes Peter the Judizing element in Galatians, despite his rather conciliatory speech in Acts 15.
A real problem with the view of Bauer is that it makes Paul an independent apostle who is the only one that fully understood the teaching of Jesus and the mission to the Gentiles. While this is quite similar to the view of Paul in some more conservative Dispensationalist circles, it does not reflect the variety of thought in the Jewish element of the church. The situation was not “either Peter or Paul.” Peter seems more moderate than James, Barnabas and Silas are a step further towards Paul.
Bauer also seems to have thought that Paul was in continual conflict with the Jewish Christians in Jerusalem. This does not seem to be the case, although one might describe the situation as “cool” between the Gentile mission and the Jerusalem church based on Acts 21.
In 1865 J. B. Lightfoot argued against Bauer and the Tübingen school. The Judaizers were not authorized at all by Peter or the Jerusalem church, although the Jerusalem church were slow in stopping them. The Jerusalem Church wanted to find a way to compromise between the radical teaching of Paul and the traditional teaching of the Judaizers. J. F. A. Hort suggested that these Jewish opponents of Paul were lead by James, although mistakenly so. James himself did not authorize the teaching in direct opposition to Paul, but his followers took James’ example of a Law-keeping Jewish Christian to the logical extreme and forced Gentiles to keep the law.
More recently, Robert Jewett argued that the Jewish opponents of Paul in Galatia were from the growing Zealot movement of Palestine . The Zealot movement was a rather radical anti-Rome movement that sought strict obedience to the Law for all Jews. Any Jews that were “Gentile-sympathizers” were the enemy. These teachers sought to supplement Paul’s teaching, according to Jewett, by teaching a form of perfectionism to counter the libertine paganism from which they were converted.
It is perhaps the statement made by Paul in Galatians 6:12-13 that gives us an insight into who the false teachers may have been. They are people that think that by compelling Gentiles to be circumcised they might avoid persecution for the cross of Christ. Likely Jewett’s theory has some merit; some Jewish Christians thought that by making Gentile Christians conform to the basics of the Law they might avoid persecution by the growing radical elements of Judaism.
Galatians 6:12-13 It is those who want to make a good showing in the flesh that try to compel you to be circumcised—only that they may not be persecuted for the cross of Christ. Even the circumcised do not themselves obey the law, but they want you to be circumcised so that they may boast about your flesh.
Who were the Judaizers, then? Jewish Christians, likely Pharisees according to Acts 15, who, with good intentions, sought to supplement Paul’s gospel by requiring that the basics of the Law be followed: circumcision and food laws. Perhaps the real issue at stake here is the status of the Gentiles within the people of God. Could an uncircumcised Gentile be part of God’s people along with Israel? Could a person be faithful to God and not keep the key elements of the covenant?
Paul reversed this argument in Galatians: can a Gentile be a member of the people of God and allow himself to be circumcised? Can a Gentile be “free in Christ” and keep the Jewish laws concerning food, festivals, etc.? The answer in Galatians is a resounding no.
A potential problem here is the value of Galatians for contemporary Christians. If the Judaizers were solely interested in converting Gentiles fully to Judaism, then what is the contemporary application of the book? How do we get from Judaizers to “Church Legalists,” as most contemporary preachers do with this passage?
 Robert Jewett, “The Agitators and the Galatian Congregation.” NTS 17 (1971) 198–212. See also Howard, G. Paul: Crisis in Galatia, 1–19.
[NB: This is a re-post of something I wrote in 2009 as part of a survey of the book of Acts. Since Acts 15 and Galatians 2 both concern the Judaizers, I have re-posted my earlier essay with little change other than the final paragraph.]