I think the important thing for everyone to keep in mind is that "Judaism" has been many things, and currently is many things. It is also worth remebering that despite this multiplicity, what can definately be said of all "Judaisms" in our day, is that they are a reaction to the birth and diffusion of the Church of Christ throughout the world.
Before the advent of Christ and the birth of the Church on Pentecost, there were many "schools" of thought in Judaism - literally the religion of the Judeans/Judahites (with a few Benjaminites and Kohanime/descendents-of-Aaron thrown in), given that the rest of the Tribes had been dispersed throughout the world and assimilated amongst other pagan nations centuries before the birth of our Lord.
Among those schools, were many who entertained ideas (or at least had a great openess to ideas) which would be foundational in the early Church. That same openess does not exist anymore, since those who persisted as "Jews against Jesus" had to shore up their doctrinal system against the teachings of the Church. This is important to understand, because if one mistakenly takes modern "Judaism" as a guide for their understanding of "Old Testament religion", they may end up with the misunderstanding that the Church and Her dogmas is some strange imposition upon the ancient Hebrew religion, and had to have gotten it's ideas from some outside source.
This establishment of impediments (by the Rabbis) to stop Jews from coming to faith and being Baptized took many forms. Whether it be the medieval credo of Maimonides (which is accepted, at least by "Orthodox Jews" as a sort of "mere Judaism", the minimum for belief) which so defined monotheism as to exclude Christian Trinitarianism or the Incarnation, or earlier corruption of sacred texts which contributed to what is now viewed in Judaism as the authoratative Hebrew Bible (the Masoretic text - a text which conspicuously differs with other manuscripts where "prophetic-messianic" texts are concerned, or those which indicate distinctly Christian dogma)...etc., the consequence of them has been all the same - Christ and His Gospel are understood by most modern Jews to be an entirely foreign phenomenon.
What is very interesting though, is that while "officially" Judaism has taken doctrinal postures which exclude Christ, the reality is that in the life of Jews since the birth of the Church has been marked by movements and rabbinical eschatological speculation which show that a lot of those "Christian ideas" are not so alien to the Jewish consciousness, even after centuries of attempts by their leaders to keep them from the Holy Cross.
For example, while the Lubavitcher Hasidim are in reality quite anti-Christian, there are many amongst their number who believe their late Rebbe (a "Rebbe" in Hasidism is a sort of supreme spiritual leader...considered to be a living sage), Menachem Schneerson, is not only the moschiach (Messiah) but...
- that he will return from the dead to redeem the Jews and usher in the "messianc age".
- and many of these Schneerson-Messianists believe the late Rebbe was in fact God Himself!
While the deified messianism of this segment of the Chabad movement is strongly spoken against by other Jews, it's interesting that such ideas still seem possible to extremely Torah-observant, religious Jews, who obviously feel they have some biblical/traditional/mystical justification for their thinking.
Something similar occured a few centuries ago in the case of the failed 17th century messiah, Sabbatai Zevi. His claim to being messiah, unlike that of Schneerson, was believed by many Jews, all around the world, even outside of his immediate circle of followers. Also, like Schneerson (in fact, it would seem more so) he was believed to have been Divine. This, imho, is another manifestation of a wavelength of thought, integral to ancient Judaism, which the Rabbis for all of their effort, were not able to completely purge from the Jewish psyche and esoteric tradition.
Like St.Paul, I still have not lost hope for the redemption of the Jewish people. There's a strong tradition in Christian eschatology, that the complete conversion of the Jewish people to our blessed Lord, will occur in the final days of this present age (just before His glorious return.)