God was free to choose some people from among the Jews to have a true spiritual relationship with him. In the same way, he was free to choose some people from among the Gentiles (non-Jewish people) to be saved. God was not limited by ethnic background.
Paul supports this point by quoting the prophet Hosea. Hosea spoke about the ten northern tribes of Israel. These tribes had rebelled against God and were under his judgment. Even so, Hosea said that God would show them mercy again.
Paul sees a wider principle in this prophecy. Just as God renewed his mercy to disobedient Israelites, he can also show mercy to Gentiles.
who are not My people: See study note on 10:19.