The problem the churches of Galatia were experiencing wasn’t a thorough-going legalism (trusting in their own works to save them)—it was a warped nationalism. They had been swayed by those had who appeared not long after Paul left the region into thinking that the only way they (Gentile disciples) could fully experience Jewish blessings was through adopting Jewish ways. After all, salvation was from the Jews—Jesus had said so Himself (John 4:22). And of course, He was Jewish. The situation was something like what it would be if someone were baptized today and then told they must become an American citizen to be part of the kingdom of God. They would in effect be nationalizing the gospel and placing parameters on it that God never intended.
Unlike Paul and many other Jewish disciples who followed the law (or parts of it) to honor their heritage and influence Jewish people who weren’t following Jesus, the false teachers’ intent and understanding was that this was part of obedience to the gospel (Galatians 1:6-7). Still, it wasn’t legalism—they weren’t trying to merge Christ’s sacrifice with their good works, they were trying to join the cross to the Torah, baptism into Christ with circumcision into the Mosaic covenant, and Christianity to Jewish nationalism.
But of course, anything added to Christ’s sacrifice subtracts from it and that’s the reason for Paul’ non-negotiable stance in the letter. When they gathered on the Lord’s day (see 1 Corinthians 16:1ff), it was as the body of Christ—not as the people of Israel. And when they took communion together, it was to memorialize the death of Christ and all that meant—not their deliverance from Egypt. This is why Paul is death on circumcision (5:2ff). The Galatians weren’t considering receiving it for hygienic reasons, or as Timothy did—to take away anything that might distract from them sharing the gospel message with others (Acts 16:1-3; 1 Corinthians 9:19ff). They were doing it because they were convinced it was necessary for their right standing with God.
With such an act they would be saying in effect that Christ’s work on the cross was had to be buttressed by Judaism. It was something like someone giving you a new car and then you replacing its engine with the one worn-out one from your old car. They were speeding right past the glorious cross for a worn-out covenant given to the Jewish nation.
There are a lot of parallels between the Galatians and Hebrews letters. In Galatians, it’s Gentile believers contemplating Judaism, while in Hebrews it’s Jewish disciples considering a return the temple and its sacrifices. Compare Galatians 5:2-4 with Hebrews 10:26-31 and note the equally severe tone in both cases. Both groups are defecting from Christ by turning their back on the efficacy of His sacrifice.