The New Testament makes it evident a "real" Jew is someone who has believed on the Lord Jesus Christ/has been "born again", regardless if they're of Jewish descent.

- NOT ALL ISRAEL ARE OF ISRAEL -

... They are not all Israel who are descended from Israel ...

Romans 9:6, Legacy Standard Bible

“... He is a Jew who is one inwardly; and circumcision is that which is of the heart, by the Spirit, not by the letter ...

Romans 2:29, LSB

- JEWS OF SATAN -

“... Those who say they are Jews and are not, but are a synagogue of Satan

Revelation 2:9, LSB

“ [Jesus speaking to certain Jews] You are of your father the devil...”

John 8:44, LSB

- BECOME A CHILD OF GOD -

“... As many as received Him [JESUS CHRIST], to them He gave the right to become children of God, even to those who believe in His name ...

John 1:12, LSB