The last post in this series was here.
At the very least, Paul was not popular with the believers in Jerusalem. Acts 21 gives us a picture of his unpopularity there just after he had written Romans from Corinth and arrived in Jerusalem. He arrives with an offering for the churches, one he has been collecting from the various places he has ministered in Greece, Macedonia, and Asia Minor (modern day Turkey). And Acts tells us that James and the elders took him aside when he arrived to strategize in relation to his opposition (21:17-26).
James and the elders inform Paul that the bulk of believers in Jerusalem are very conservative indeed when it comes to the Law. They have heard rumors that he was teaching Jews among the nations to abandon the Law of Moses (21:21). They have heard he is telling Jews not to circumcise their children and do other key Jewish practices. The elders strategize with him to participate in a vow certain men have taken, to pay for their sacrifices and other elements of the vow at the temple. The goal is that everyone will see that Paul himself does in fact keep the Jewish Law as a Jew, despite certain exceptions they have made for Gentile believers.
Paul confirms in Romans that false rumors did circulate about him. In Romans 3:8, Paul alludes to people who sum up his teaching as, "Let's do evil so that good can come." This slogan seems to be their version of Paul's teaching on "faith rather than works of Law" making us right with God. He makes it clear in Romans 6-8 that he does not advocate sinning more to show how much more grace God has. But by sinning here, he almost certainly does not mean keeping the parts of the Jewish Law the Jerusalem Christians of Acts 21 are concerned about--circumcision and matters of ritual purity.
Paul had been sparring with this "denomination" of Christians for a long time by the time he came to Jerusalem, perhaps some time around AD58. Acts is much more favorable to them than Paul himself was. Paul considered them "false brothers" (e.g., Gal. 2:4), but Acts treats Paul's opponents on these issues as if they are just as much believers as he is (e.g., Acts 15:5; 21:20). About ten years earlier he had privately presented his teaching on Gentiles to Peter, James, and John because he knew some believed you could only be saved if you fully converted to Judaism (Gal. 2:1-10). They seemed to prefer that Gentiles convert, but they did not force them to (Gal. 2:3).
He almost certainly lost an argument at Antioch with Peter over how Jewish and Gentile believer might eat together (Gal. 2:11-14). James had sent messengers there to make sure that Jews were still keeping purity rules, even though Gentiles could be saved without being circumcised. Paul had disagreed. He saw the purity rules as irrelevant to what made a person right with God. In a very real sense, he really did advocate that Jewish Christians abandon some of their customs so that they could fellowship with Gentile believers.
This argument probably stands as much or more in the background of the break up of Paul and Barnabas as a ministry team as Mark did, even though Acts only tells us about Mark. Paul would have almost certainly told the Galatians that the other side conceded--if they had. Rather Paul seems to have embarked with Silas on his second missionary journey somewhat on the outs with the churches of Jerusalem and Antioch.
Acts 15:23-29 seems to give the solution James and the Jerusalem elders came up with on the issue of Jew and Gentile eating together. If Gentile believers would not bring meat that had been offered to another god, if they would not kill the meat by strangling, so that the blood stayed in the meat, if they would not be sexually immoral, then Jewish and Gentile believer could eat together. But as far as we can tell, Paul ignored most of these instructions--all except the sexually immoral bit. When the issue of meat sacrificed to idols came up at Corinth, Paul adopts a "don't ask, don't tell" policy. Don't ask where the meat came from and eat it with thanksgiving (1 Cor. 10:23-30).
The book of Galatians is all about Paul's disagreement with other Christians who insisted Gentile believers become circumcised. Although others date it much earlier, we have pictured it while Paul was at Ephesus on his third missionary journey. We get his "first draft" of a response to his detractors, his understanding of how a person can be in right standing with God and exactly what the purpose of the Jewish Law is. Again, although others date it differently, we have pictured Paul writing Philippians at Ephesus as well, just a little bit later. In Philippians 3 Paul tries to warn the Philippians ahead of time about his opponents, "those who mutilate the flesh" (3:2), those who insist Gentiles must be circumcised.
So by the time Paul writes Romans, he knows his opponents and their arguments well. He knows what others are saying about him and he has been perfecting his response for years. He knows what response worked with the Galatians and what did not. The bulk of Romans is thus Paul's most developed defense of the gospel message he has preached among the Gentiles. It is not a "compendium of Christian theology" in the sense we would write one today. It is still a letter written in a certain situation to address a situation. But Paul writes it as an introduction to what he actually believes and teaches, and in that respect it is the most systematic presentation of his theology on these particular issues that we have.
As Rome had both Jewish and Gentile believers, it is reasonable to assume that Paul anticipated that both Jewish and Gentile Christians would read Romans. However, the bulk of his rhetoric addresses Gentiles, in keeping with Paul's sense that he is apostle to the Gentiles, not to the Jews. In 1:13 Paul says he wants to have some fruit among them just as among other Gentiles. In the next verse he does not divide those he feels responsible for into Jew and Gentile but into "Greek and barbarian"--a way of dividing up the Gentile world. In Romans 11:13 explicitly addresses the Gentiles as the audience and warns them not to get cocky about God's current favor on them. Paul's address to a Jew in Romans 2:17 is more about what someone might say rather than a direct address to someone in the audience. So Paul could have expected that some Jewish believers would read Romans, it seems mostly to address Gentile believers, in keeping with Paul's own sense of the mission to which God had called him.
So Romans is a defense of the gospel Paul preached among the Gentiles, with a view to the objections and arguments his detractors had used against him, particularly his detractors in Jerusalem and Antioch. He goes about to show that all have sinned, both Jew and Gentile, and thus that both equally rely on God's grace to be accepted by Him (Rom. 1-4). He shows how Christ's obedience has undone the sin of Adam for everyone, including both Jew and Gentile (Rom. 5). He addresses the question of just what the purpose of the Jewish Law was in the first place and in the process the accusation that he is advocating that Christians sin (Rom. 6-8). And he steps back and speaks about God's plan and how Jews and Gentiles fit into it (Rom. 9-11).
You can see the degree to which the "Gentile question" dominates the entire letter. How is it that Gentiles can be part of the people of God if they do not convert to Judaism? Romans was not, as Augustine and later believers made it, an abstract theology of how to get saved. Any time Paul mentions the law, he has in mind some part of the Jewish Law, not some abstract moral law. And when Paul talks about works, the parts of the Jewish Law that most separated Jew and Gentile were never too far away. Romans is thus Paul's most developed response to his detractors.