There are lots of saved Jews, called Fulfilled Jews. They see that Jesus came to them, fulfilling their law. They recognize the OT prophecies of Jesus which have been rejected by mainstream Jews. They're there for all Jews to read but re ignored. They've accepted Jesus as Lord.
When someone today refers to a Jew, he's referring to someone who 1) claims a connection to Abraham through descent, and 2) adheres in some sense to the Judaic religion/culture/identity grounded in the Talmud. If you adhere to the Talmud in any sense, you are not a Christian, since the Talmud preaches against Christ, and even applauds his crucifixion.
Converts to Judaism, therefore, aren't Jews. They are non-Jewish practitioners of the Judaic religion (e.g., Madonna). If they intermarry, their descendants may become Jews, but they, themselves are not.
Someone with Jewish ethnicity who has accepted Christ (and rejected the Talmud) is not a Jew, but a Christian.
