I'd flip the script. Are Gentiles who have accepted Christ, Jews? Are Gentiles who have chosen Christ his chosen people, or not? If not, why not?
His
Possibly.
But if so, if Christians are the real Jews, then "Jews" who reject Jesus are "those who are of the synagogue of Satan, who claim to be Jews though they are not, but are liars" (Revelation 3:9)
I think this is what John meant. That to accept Jesus is to be a real Jew. And to reject Jesus is to cease being a Jew.
Which is not a pleasing thought to those who today call themselves Jews.