God's Chosen People.
It's right in those 3 words.
The Jews did not choose God, God chose them.
Why? Because they were such good people?
Not necessarily. He chose to reveal Himself to them. Abraham accepted God.
God chose Abraham to fulfill His promise of a Messiah.
That promise has been fulfilled thru Jesus.
But since then there have been people who have accepted Jesus as the Promised Messiah and people who have rejected Jesus as the Promised Messiah.
That is the dividing line.
So it doesn't matter what people call themselves.
What matters is what God calls them.
In the end He will call them His own, or He will reject them and say that He doesn't know them.