Most of the time, we tend to read Paul through a Lutheran lens. Luther, perhaps for his own polemical reasons, interpreted Paul as setting grace (good) against law (bad); the Jews emerge as the bad guys - let's face it, the Gospels do let the Romans off the hook for the Crucifixion and blame the Jews instead - and in Luther's view, Jesus replaces the impossible Law with the glorious light of grace. Unfortunately, this is a serious misreading of Paul.
Paul is, after all, a Jew, with impeccable credentials. He's a Benjaminite , a Pharisee, a Hebrew of the Hebrews (Philippians 3:5; I'm only citing Paul's testimony here, and ignoring Luke's portrayal of Paul in Acts). The Hebrews were the Palestinian, Aramaic-speaking Jews, which might perhaps contradict Luke's testimony that Paul was from Tarsus, but in any case, he comes of Jewish stock, and he's no mere convert. He's been been based at the Antioch church, which was, by all accounts, rather more liberal than the mother church in Jerusalem, but he's been sent by Jerusalem to go to the Gentiles (Galatians 2:9). Both Paul and Luke make it plain that, at this time, Jerusalem was where the decisions were made.
Paul has come to Galatia, whose people were Hellenised Celts, with the message of Jesus. He's established a community of people, now essentially Greeks, though still with the Celtic heritage, who followed a Jewish messiah, under Roman rule. We needn't be surprised that this multicultural mishmash led to a few tensions!
The Jews, of course, were a tolerated minority, granted protection within the Roman empire, and allowed to follow their own religion in peace, to the point where it was legal for a Roman citizen to be a Jew. At this time - Galatians was written sometime between AD 48 and the mid-50's - the Jews had lived peacefully within the Roman empire for generations, since Pompeius Magnus captured Jerusalem in 63 BC, and established a puppet kingdom there. They offered daily sacrifice for he Emperor in Jerusalem, and were not expected to sacrifice to him.
They were however, a minority, and as such may well have felt insecure within the Hellenistic world. In the 160's BC, there had been an attempt to integrate Jerusalem, with the establishment of a syncretistic cult which identified their God with Zeus Olympios. In 41 AD, Caligula, who had been brought up partly in the east, and took divine kingship extremely seriously, ordered that a gilded statue of himself be set up in the Temple, so that the Jews could sacrifice to him. The governor of Judea prevaricated, and Caligula was murdered before the order confirming the erection of the statue could arrive in Jerusalem. Lingering worries emerge in the Gospels, which refer to the Abomination of Desolation (Mark 13:14, Matthew 24:15; the term comes from 1 Maccabees 1:54). Evidently there was a feeling that, sooner or later, someone was going to put an idol in the Temple and make Jews worship it once again.
A diaspora community, in daily contact with their Greek neighbours, would have been doubly insecure. Then Paul came along and started a group of pseudo-Jews; they worshipped the Jewish god - perfectly legally, of course; it's not clear when the first anti-Christian legislation was passed, but it was long after this - but they did none of the things which marked Jews as Jews. They weren't circumcised, didn't keep Sabbath, and their meat probably wasn't kosher. In that case, as secular slaughter didn't exist, it would have been sacrificed at the local temple. They weren't following pagan cults, but they weren't Jews either. So what were they? It must have been a confusing situation.
Someone - either people sent by James, mentioned in Galatians 2:12, or the local synagogue - had a simple solution. They should convert, get themselves circumcised, and become proper Jews. If they did so, everyone would know where they were, any tensions would soon settle down, and in any case, there was an advantage to being a Jew. They'd be full citizens in the Kingdom when it arrived, rather than tolerated strangers and aliens, righteous before God, but, as it were, posessing permanent leave to remain, and nothing more. It was, after all, going to be a Jewish kingdom, under a Jewish God.
No ancient Jewish document claims that Gentiles can't be acceptable to God as Gentiles. It would be a little difficult for anyone to say that, considering the number of righteous Gentles in the Jewish scriptures. Rather, the Mishnah, from the end of the 2nd Century AD, takes the view that God gave seven basic Noahide Commandments to Noah, and through him to all humanity. Any Gentile keeping these would be righteous before God. The commandments of Moses, because these were only given to the Jews, so onlyJews had to keep them. Most likely, this was only a formalisation of an existing conclusion; the New Testament, written earlier, takes a similar view.
In Acts 15, Luke gives us an account of the Jerusalem Conference, where James, the top dog in the church there, has the last word:
"It has seemed good to the Holy Spirit and to us to impose on you no further burden than these essentials: 29 that you abstain from what has been sacrificed to idols and from blood and from what is strangled and from fornication. If you keep yourselves from these, you will do well."
Luke wrote at the end of the First Century AD; Paul, writing earlier, never gave a formal list of requirements, but his advice to Gentile followers of Jesus is comparable. Galatians is his earliest response to the issues, and lacks the carefully thought-out arguments of Romans. Rather, Paul has reacted with a furious rant. At one point, he got so worked up, he wished the circumcisers would castrate themselves (5:12). There's an implied comparison here with the priests of the local Magna Mater cult, who were eunuchs; this could only have been seen as a terrible insult.
In the crucial passage, though, he comes up with something which was, as far as I've been able to discover, new.
In Christ Jesus you are all children of God through faith. As many of you as were baptized into Christ have clothed yourselves with Christ. There is no longer Jew or Greek, there is no longer slave or free, there is no longer male and female; for all of you are one in Christ Jesus. And if you belong to Christ, then you are Abraham's offspring, heirs according to the promise. (Galatians 3:26-29)
God is no longer a Jewish God; the Kingdom is no longer a Jewish kingdom. Rather, Jew and Gentile enter on an equal basis, via their defferent routes. Paul continues to develop this idea through his letters, most notably in Romans, and it's this that brings him into conflict with his fellow Jews. The familiar distinctions of the ancient world have been relativised; they can no longer be absolute, since before God, they are meaningless. Each, therefore, should remain as they were. The Jew should obey the commandments of the Law, since they are binding on them, and the Gentile should continue to ignore them, since they were never given to them. Their final status before God, which was Paul's main concern, would be the same.
Today, we often take this for granted. Our culture is far removed from those in which Paul moved; slavery is effectively invisible, though it still exists, and despite the continuing sexism of our culture, women can become Prime Ministers. Many Jews are so well integrated into the wider culture that they are almost invisible. We take it for granted that God makes no distinctions, and assume that this passage refers to social justice.
This isn't entirely wrong. If God, say, treats men and women the same, it would be wise for those who claim to be his worshippers to do likewise, and to do what they can to ensure that others do as well. If we don't, God may have something to say about it. In that case, to borrow one of Matthew's favourite themes, there will be weeping and gnashing of teeth. However, this is a secondary implication of the text, not what Paul is actually saying.
Obviously, the church didn't invent sexism. It has, hoever, often justified and maintained it, and developed its own version, creating religious barriers to women, who, in some churches, cannot serve as priests or ministers, and sometimes cannot even set foot in the sanctuary. Equally, we didn't invent racism; it grew out of the slave trade. We did allow the church to be used for some centuries, to legitimate it, and thus to allow it to continue its development.
Antisemitism, however, was the invention of the church. Paul tells us that there is now no barrier between Jew and Gentile; our response has been to pick up the way the Gospel authors, for their own political reasons, exonerate the Romans for the Crucifixion, and blame the Jews instead. We developed the nonsense that the Jews crucified Jesus, and in doing so, laid the foundation for the Holocaust, and all the other pogroms the Jews have suffered. We also, for that matter, laid the foundations for apartheid. Instead of demolishing the stupid barriers which divide humanity, we developed new ones.
God, however, only created one human race, and gave us only one world to live in. All the things which divide us, and justify one group of people in trampling on another, whether the victims are black people, Jews, Arabs, women, or whoever, are ultimately incompatible with our Chrisitian profession. If we're all equal before God, then we need to ensure, firstly, that everyone is equal within the church, which represents God on earth, and secondly, that we use whatever influence we have to oppose everything which makes people unequal out there in the world, and which leads to discrimination.