Was Peter a pig-headed Jew who should have known better about the Gentiles?
No. Peter was not a pig-headed Jew who should have known better; he was a Jew who knew what was expected and was absolutely in accord with the program thus far. Gentiles were still viewed as dogs, so only the supernatural vision, the men at the gate, and the Holy Spirit's command moved him to go.
Les explains that Peter doubted what the vision meant, but God's timing was perfect: the men sent from Cornelius arrived at Simon's house just as Peter came through the vision. The Holy Spirit told him to go with them, doubting nothing. Les asks whether Peter would have gone to Caesarea without the supernatural environment—the trance, the men at the gate, and the Spirit's voice—and answers no, because as far as Peter was concerned, Gentiles were still dogs and God could have nothing to do with them. Yet Les reminds people that Peter was not a pig-headed Jew who should have known better; he was a Jew who knew what was expected, not out in left field, but in accord with the program thus far. The context points back to Matthew chapter 10.