Please become informed of history before writing posts like this.
Jesus couldn't have been Christian. He couldn't follow himself. He lived and died an observant Jew, as did his family and friends. And before Paul, Nazarene Jews did not believe in the Trinity or that Jesus was G-d incarnate. They merely believed he was the Messiah. When the whole "G-d" thing came up many Nazarene Jews didn't approve and even left.
The ones that didn't broke off from the main tenets of Judaism, thus no longer being Jews.
And besides that, the "New Testament" applies in no form to Jews. That is a CHRISTIAN book, not a Jewish book. We have NO New Testament.
And in the Torah, Jesus isn't mentioned at all. It just says that saying you're G-d is blasphemy and so is saying G-d can be more than One and Whole in any way, shape or form.
However, in short answer, true Nazarene Jews WOULD have been seen as Jewish. They celebrated Jewish holidays, they followed the Jewish mitzvot, they did not believe in Trinity or that Jesus was G-d, and they didn't condemn people who didn't believe Jesus was the Messiah.
The changes made by Paul, the condemnation of those who do not believe in the Messiah, the belief in a Trinity or that G-d is anything but One and Whole, etc., etc... THOSE things broke off Christianity and Judaism.
In another world, Islam might have been merely a branch of Judaism. You realize one of the main things that cut the divide was a misconception that we had a long time ago that Muslims worshipped idols (ultimately it was decided there can be no "additions" so therefore Muslims cannot be considered Jewish - just righteous Gentiles like everyone else including Christians). Likewise, in another world without Paul's form of Christianity, Christianity would have either died out or become a mere sect of Judaism. But it broke off too much. There is no sect of Christian (accepts Jesus as the Messiah) that maintains all the tenets of Judaism anymore.
Look at it this way - in Orthodox Judaism I am not Jewish. Conservative Judasim doesn't observe the mitzvot at a deep enough level to be considered Jewish by Orthodox standards. Orthodox used to not mind Conservative until we began doing some major "no-no's" involving egalitarianism, and more importantly, things like driving on Shabbat. But I share the same tenets of faith - Moses, Abraham, one G-d, 613 mitzvot, teshuvah, shivah, etc., etc.
Even with all those similarities, I'm only Jewish with liberal sects (or almost Jewish anyway). Judaism knows what it is, more or less. There are standards.
In every generation, there is a great Jewish scholar that some people follow believing that he is the Messiah.
But the difference between Jews and Christians is that when a theoretical Messiah dies in Judaism and he hasn't fulfilled the prophecies... They stop believing he was the Messiah. They go back to waiting for the Messiah. Because it's supposed to happen in one lifetime. And they don't believe that he's G-d, either. The instant it involves a "second coming" instead of one lifetime, it's over.
RJ and Paperback Writer, your answers are always so nice and succinct. Absolutely right, of course.