Of a truth I perceive that God is no respecter of persons. -- Acts 10:34 (KJV)
Peter walks into a Roman officer's house, opens his mouth, and the first sentence out of him is the whole sermon: God shows no favoritism. He does not build toward it. He leads with it, standing in a room he would have called forbidden a week earlier, facing people his training had taught him to count unclean.
The wall between Jew and Gentile did not fall because the Gentiles cleaned themselves up. Cornelius passed no test. Nothing about him changed between the angel's visit and Peter's sermon. Peter did. Standing in that house, he saw what had been true since God first called Abraham: that through one man all the families of the earth would be blessed. The promise had been global from the opening, reaching past Israel's border since the covenant began, and the church only needed someone to see it.
The Favoritism Did Not Stay in the First Century
The wall Peter walked through is still standing. It shows up as a preference for the people who vote like us and worship like us. We rank the room before God has said a word to us about anyone in it. Peter ranked Cornelius for years, and then one vision and one sermon later the ranking fell apart, because he came to agree with what God had been saying the whole time. God pours out His Spirit on hunger. In every nation, the one who fears God and does right is welcome, and God attached no fine print to that.
Picture where Peter stood when he said it. On the coast at Caesarea, a Roman household in front of him, the Mediterranean at his back, and past that water every nation the gospel had not yet touched. He was facing the old enemy with his heels to the whole waiting world.