I think Paul is saying that a Jew is a Jew from the heart, from the inside out, who values his heritage, knows where he came from, and followed in the ways of his people -- not just someone who had Jewish blood. Many back then and throughout history have been Jewish in name and blood only and cared little about Torah, and Moses, and Isaiah, their heritage, their covenants, and the promises to them, the things that made them uniquely Israel before God.
Gosh, I think that is a terrible reading of the Gospel. Paul isn’t criticizing Jews for not being better Jews. He’s criticizing Jews for not believing in the only name that saves, Jesus Christ.