What did Peter say was unlawful for a Jew to do with Gentiles?
Peter said it was an unlawful thing for a Jew to keep company with or come unto one of another nation. He also indicated it was unlawful for a Jew to go into a Gentile's house, which is why he was uncomfortable entering Cornelius's house. God later showed him not to call any man common or unclean.
Les explains that when Peter spoke to Cornelius, he said, "You know that it is an unlawful thing for him that is a Jew to keep company or come unto one of another nation." Peter was coming back to the law, recognizing the Jewish law forbade such association. He was uncomfortable going into Cornelius's house because it was unlawful for a Jew to go into a Gentile's house. But Peter added that God had showed him in the vision of the sheet with clean and unclean animals that he should not call any man common or unclean. Les points out this was not just about food but about the human race. The apostle of the Gentiles was saved in chapter 9, and the gates were being opened to Gentiles, expanding further in chapter 11 and the missionary journeys in chapter 13.