At issue here, I would suggest, is largely an issue of semantics.
Jesus was a Jew, and never appears to have given any indication in the Gospels that he regarded himself as having left his faith or of starting an entirely new one. As a previous poster noted, he spoke of himself as “fulfilling Scripture”. At various places in the Gospels he objects to strict adherance to Jews laws or customs but definitely does not say he is rejecting Judaism. An example is when he is challenged because he and his disciples do not ritually wash their hands before eating.
In the early days of the Church there was friction among Jewish and Gentile converts over the degree to which conventional Jewish customs needed to be preserved by believers; St. Paul discussed the issue of whether circumcision was still was required. I, for one, get the impression that he was writing as a Jew to people who were converting to a new Jewish movement.
Based on the same evidence and following pretty much the same logic, one can instead conclude that Christianity is a whole different religion which grew out of Judaism, or is a variant or extension of conventional Judaism.
In normal speech, most people imply the former: that Christianity and Judaism are altogether distinct. I’m a Catholic who grew up in a largely Jewish neighborhood. I never took a poll, and it wasn’t something we had cause to discuss much, but I recall knowing as a child that some of my Jewish neighbors regarded Jesus as a great rabbi or even a prophet. Still, as a matter of courtesy, I would never have referred to myself when speaking with them as a fellow Jew.
As for the latter view, that to be a Christian is to be a kind of Jew, some years ago I heard the novelist Andrew M. Greeley, who is a Roman Catholic priest, interviewed on a radio talk show. A caller who identified himself as Jewish said he was glad that Pope John Paul II referred to Jews as “our brothers in faith”. Greeley then remarked that when you came right down to it, Christianity is a Jewish faith. There are, of course, countless bigots–Christian and Jewish–who would object to that.
Religious terms are, in fact, awfully equivocal. There are Unitarians who say they are Christians and Unitarians–often in the same congregation–who say Unitarians are not. I knew a very nice and extremely well-educated woman who was a member of the Bahai faith who said she didn’t understand why a local Pentecostal minister had such animus against her people since, after all, they are Christians too.
As for the term Gentile, it’s standard meaning is a person who is not Jewish. On the other hand, among Mormons, it means a person who isn’t Jewish or Mormon. When the LDS Temple was opened in St. Louis, non-Mormons were permitted tours for a limited time. A friend of mine who is Jewish took the tour, and ended up as confused as heck by the way the guide was talking.