The term "the people of God" always implies a distinct connection. In Genesis 12, God commanded Abram (later Abraham) to leave his homeland in favour of a new one that He would show him. God promises Abram in Genesis 12:2 that he will make him into a great nation and bless him, as well as make his name famous and make him a blessing. The first group to be identified as God's people, this country would later become known as Israel.
I have put my words in your mouth and covered you with the shadow of my hand, I who established the heavens and laid the cornerstones of the earth, and who declares to Zion, "You are my people," is what God says to Israel through the prophet Isaiah. (16) Isaiah 51: In a prophecy to the nearby Gog-and-Magog nation in Ezekiel 38:14, God further affirms Israel as His people.
Do non-Jewish people who follow a Jewish Messiah (Jesus Christ) qualify as God's people? Yes. Jesus did not only come to save Israel, but all of mankind (Romans 1:16, 10:12; Galatians 3:28). God's relationship to His people extends beyond just His calling; they also refer to Him as their God. I know, my God, that you examine the heart and are pleased with virtue, David says. I gave all of these things voluntarily and with good intentions. And I am now glad to see how willingly your people here have contributed to you (1 Chronicles 29:17). Here, rather than by their ethnicity, God's people are distinguished by their readiness to give themselves to Him.
Anyone who confesses Jesus Christ as Savior and Lord joins God's people. The connection was not established through charitable work or church attendance. The decision to follow God alone is a conscious one. Because of this, Mark 8:38 and 2 Corinthians 6:16 both suggest that a decision must be made. And when we decide to embrace God, He chooses to do the same for us. We are then truly His people.