Claim #1: Jews can retain their Jewish Identity once they convert
In their attempt to convert Jews, missionaries claim that one can remain Jewish while practicing Christianity. The use of terminology such as "Messianic Jew," "Hebrew Christian," and "Jews for Jesus" is but a deceptive attempt to represent converted Jews as Jewish.1 In fact, missionaries even go so far as to claim that a Jew who accepts Jesus (or "Yeshua," as they call him) is a "completed Jew," implying of course that all other Jews are incomplete.
The misrepresentation and deception employed in this attempt to disguise the seriousness of a Jew's conversion to Christianity is similarly reflected in the widespread misuse of Jewish symbols and customs, in the fabrication of Jewish texts, and in the misrepresentation of the background and Jewish education of many "Hebrew Christians." Numerous "Hebrew Christian" leaders dishonestly refer to themselves as "rabbis" and to their places of worship as "synagogues."2
These tactics are employed in an attempt to render their version of Christianity more palatable to the Jews they seek to convert. However, in the words of one of the numerous Christian groups which condemn "Hebrew Christianity," "These proselytizing techniques are tantamount to coerced conversions and should be condemned." (From a formally adopted statement issued by the Interfaith Conference of Metropolitan Washington, D.C.)
The Jewish Response
The fact remains that, regardless of superficial attempts to sound Jewish, the term "Hebrew Christian," or "Jews for Jesus," is an oxymoron and a theological contradiction.
So-called "Hebrew Christians" argue that a person who is born Jewish can never lose his birthright or heritage. However, the Bible teaches that your beliefs do influence your Jewish status and that a person who was born a Jew can at some point temporarily cease to be called a Jew.
In the Book of Kings, Elijah the prophet is sent to rebuke those Jews who were worshiping a foreign god called Baal. In I Kings 18:21, Elijah says to them, "How long will you waver between two opinions? If the Lord is G-d, follow Him: but if Baal, follow him." In other words, you are either a Jew or a worshiper of Baal; you can't be both. The story concludes with the Jews renouncing their idolatrous ways and returning to Judaism.
From this, we derive an important lesson. A Jew who follows another religion is Jewish only to the point that he retains a spiritual obligation to repent and to return to Judaism. However, as long as his beliefs are idolatrous and foreign to Judaism, he cannot call himself a Jew. (It is important to note that a non-practicing Jew is different from a Jew who has chosen to follow a foreign path.)