In the first century, there was a big distinction based on race in the Jewish religion. Peter writes that it was common knowledge that "it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation" (Acts 10:28). There has been a long-standing policy in Judaism for a rabbi to discourage Gentile converts at least three times before joining Judaism (they explain that the Jewish religion is natural for a Jewish soul, but a burden for the soul of a Gentile). This attitude towards the Gentiles by Jewish rabbis adds context to several examples of interactions with Gentiles where it seemed that Jesus was less than compassionate at the first encounter1 (Matthew 15:22-24, Mark 7:25-29, John 4).
Paul underwent a tremendous conversion experience. Before his conversion, he considered himself to be a "Hebrew of the Hebrews" (Philippians 3:5-6) and "far more zealous for the traditions of my ancestors" (Galatians 1:13-14). After his conversion, Paul considered himself an "apostle to the Gentiles" (Romans 11:13, Acts 9:15, Galatians 1:15-16, Ephesians 3:8)
So what did this step towards racial integration look like? Well, Paul started drawing on stories and literature from the Gentile cultures to illustrate his points when he would write and preach (Acts 17:28, Titus 1:12). He started mentoring Gentile pastors (e.g., Titus, Timothy) to carry on his work when he was away or after his death. He publicly called out church leaders when they would regress towards the old way of separating Gentiles and Jews (Galatians 2:11-14).
I find it alarming that what ultimately killed Paul was his decision to compromise when it came to the distinction between Jews and Gentiles. Paul had written that in Jesus, there was no distinction between the Jew and the Gentile, had preached this message throughout the Mediterranean, and had called out church leaders who had taken steps backwards. However we find in Acts 21:17-26 that when Paul came to Jerusalem, the church leaders challenged him, asking him to perform an exclusively Jewish ceremony to demonstrate to the believers in Jerusalem that Paul was okay with the Jews having their exclusive church rituals. When Paul acquiesced against his better judgment, several non-believing Jews arrested him in the temple because they thought that one of the Jews that Paul was performing the ritual with was a Gentile (Acts 21:27-30), and that Paul was preaching that the Gentiles had to follow Jewish rituals (which couldn't have been farther away from what Paul actually thought). Because of the confusion brought out by Paul's compromise, the Romans took Paul into custody (Acts 21:34), then transferred him to a prison in Caesarea (Acts 23:23-35), then transferred him to Rome (Acts 25:12), where he was finally executed.
Paul spent his entire ministry teaching that the gospel was the same for the Jew and for the Gentile, and that the church ought to be an inclusive organization that does not prefer one over another. Paul faced tremendous opposition both inside and outside the church, and ultimately was exected because he gave into churh leaders in Jerusalem. Paul's mission to break down the barrier of racial distinction was never fully accomplished in his lifetime, and it even continues to this day. But the same Jesus that used Paul to preach this gospel of unity is just as ready to use us today as he was with Paul.
A closer look reveals that Jesus did indeed care, based on the unusual words He would use, the great distances that He would walk to encounter these people, and the fact that He interacted with them at all. ↩