Anybody who is of the faith is a Jew. Just as anyone who believes in the teachings of Christianity and professes to be a Christian is a Christian, as anyone who was born into or converts to Islam is a Muslim.
Jesus was born a Jew, his family, disciples and followers were of the faith of Abraham, the Hebrews, Israelites. Which of course did split into tribes and factions....but that doesn't negate the history of the faith.
