Is a "believer" still Jewish?
A Jew who believes in Jesus as his/her "Lord and Savior" has become a Christian. Even if not a formal member of a church group that person is a Christian theologically.
The halacha (B.T. Sanhedrin 44a) recognizes the biologic link to the Jewish people as inviolate, but also recognizes that as long as one remains an apostate one is not considered to be part of the Jewish community. A willing convert, whether formally or informally, forfeits his/her legal and social rights, which express a Jew's belonging to the Jewish people.
A Jew must meet, actively or inactively, the fundamental biblical stipulation: "You shall have no other gods before Me" (Exodus 20:3, Deuteronomy 5:7). God declares: "I am the first, and I am the last, and beside Me there is no God" (Isaiah 44:6). Surely, a belief in "God the Father," "God the Son," and "God the Holy Spirit" does not satisfy God's command even when one claims that these three distinct personages are really a tri-unity.
Even to make Jesus into "a god" but not God Himself denies God's declaration that He lone is God. Such a belief creates a dualistic system of shared divinity unrelated to the eachings of the Jewish Scriptures.