In Acts 10, Peter was confronted with his prejudice against gentiles and learned the lesson that all who came to Christ were "clean" in God's eyes and worthy of full fellowship. Prior to this, the disciples did not actively preach to the gentiles but only to their fellow Jews. Cornelius and his house were Roman gentiles but they were clearly fully accepted by God. Peter could do no less.
I hope you have found this helpful.
God bless,
Mike