Is it possible to be a Jew for Christ

From the Hebrew Scriptures, including the Talmud we can learn that the Chosen People or Israel is eternal, so the bond with them is irreversible, unbreakable and eternal, once a Jew always a Jew. As a Jew following the Jewish rebbe Jeshua should not mean that one has to give up the Jewishness, even better being a follower of the sent one of God one can become even closer to God.