Paul clearly says that a Jew is not a Jew because he is one outwardly.

..........Romans 2:28-29
For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh:
But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.