I have never once heard any Christian, fundamentalist or otherwise, claim any such thing. Unless I'm completely misunderstanding what you mean. Had Christ not been a Jew, what would he have been? This is where Universalism falls on its face. "I came not to abolish the Law, but to fulfill the Law." The Law is Jewish by definition.
Jesus, who is God, transcends religion. He is the Word. His Word is truth.
Having said that, Jesus cannot be separated from his Jewishness. It is the very foundation, the premise, through which Christ presented himself. The story of Genesis and the fall of man is actually the story of the promise of redemption through the Messiah, a new Adam, who will be sent. Genesis foretells Jesus, as does the entire underlying theme of every book in the Old Testament. The Hebrew story is the story of God revealing himself to man through the Jews and his promise of ultimate salvation. Jesus is the culmination of everything, and it requires a real understanding of the Hebrew story and the promises God made to them to truly "get it." The Old Testament was thousands of years of God paving the way for Christ so that people would be ready for him when he came. It was the proof waiting for the Man. A lot of people didn't get it, and still don't.
Can you be saved without knowing the relationship of Judaism to Christ? Sure. Salvation is grace from God. But Salvation is where our relationship to God starts, not ends. Peter and Paul fought bitterly over this question. Peter and others thought to follow Christ you had to first become a Jew. Paul disagreed. Peter eventually got it. But even Paul understood that salvation came to the Gentiles only because Jesus came to the Jews first. While we, who were not given the Law, can be saved- our salvation comes from Christ who came as a Jew to the Jews. In fact, had the Jews not rejected Christ then Peter would have been correct. We would have had to become Jews to follow Christ. This is clearly pointed out in scripture.