There's another group of Jews who actually does believe in Jesus, and Paul is pretty psyched to have them in the fold. He's one of them, after all, and he does think that Jesus came to bring the truth about God to the Jewish people. So all is well with these guys, right?
Not quite. There are some issues. Specifically with the Gentile-Christians. Many of the Jewish-Christians see their faith in Jesus as an extension of their Jewish faith. As a result, they think that anyone who believes in Jesus also has to follow Jewish law. It's the Torah, y'all, so let's start showing it some respect. All 613 mitzvot of it.
All these rules are a bit much for the Gentiles. Some of the biggest conflicts are popping up around circumcision and food. Many of the Jewish-Christians (who are already circumcised) think that the Gentile-Christians need to get snipped in order to join up. We imagine potential male converts saying, "Yeah, I like Jesus and all, but you want me to do what to my man bits?"
Paul settles the issue in true Paul style… by agreeing with everyone. That means that, while Paul thinks Jewish law is the bomb and people are totally right to be following it, he also doesn't think you have to require everyone to keep every single little commandment in order to get in good with Jesus. Living a life of faith is the most important thing.
So do you have to be circumcised? No way: "Real circumcision is a matter of the heart—it is spiritual and not literal" (2:9). It's also way less painful. In other words, it's what's inside your heart, not in your pants, that counts.
Do you have to keep kosher? Nope: "Those who abstain must not pass judgment on those who eat, for God has welcomed them" (14:3). In other words, back off, guys. God doesn't really care what you're eating. Let's stop beating each other up over ham sandwiches.
Throughout the letter, Paul is really suspicious of anyone who thinks they're better than someone else. That definitely goes for Jewish-Christians. If they think that they're earning extra points with God by checking off Torah boxes, then Paul thinks they're completely missing the point. And that is not gonna be fun to explain come judgment day.
Paul sums all this up rather nicely: "There is no distinction between Jew and Greek; the same Lord is Lord of all and is generous to all who call on him" (10:12). Preach on, brother Paul. Preach on.