This is an unofficial position. Neither the Jesus of history nor the Jesus of the Christian tradition is part of the Jewish religion.
The Jewish take on Jesus is hopelessly biased by the much more important influence and interaction of Christian and Jewish peoples on one another over the span of 2000 years. But that is not the influence of Jesus per se.
By the way, what very very few Christians realize is that Judaism in one sense is younger than Christianity. The near entirety of modern Judaism is rabbinic Judaism, which was an outgrowth of the Pharisees who were a minority group at the time of Jesus. Most Judaism 2000 years ago was priestly.
Then the Romans destroyed the second temple in 71 AD, leading to a Jewish diaspora and the rise of rabbinic Judaism as the dominant vein of the religion. In the 1938 or so years since then, Judaism has developed an enormous body of literature and scriptural and legal interpretation, principally the Talmud, it's developed major philosophical and theological and even mystical arms (with the Aristotelian Jewish rationalist Maimonides at one end and the Kaballah at the other)...
The point is that the points of origin for modern Judaism AND for Christianity happened at roughly the same time. So aside from the obvious that Jesus is simply not a part of the Jewish tradition, Judaism does not exactly have an unbroken thread going all the way back to Abraham and the life/death of Jesus happened before the catastrophe in 71 that launched modern Judaism.
I do not see why you need to go on about how Judaism is "Newer" than Christianity. First of all priestly Judaism was predominant among a section of the priestly class (Sadducee) which in rabbinic literature and other contemporary literature of the time was depicted as being a small oligarchal rule and not representative of then-mainstream Judaism. Most opinions place Rabbinic Judaism among Ezra, which is well before Christianity or even greko-roman rule over the area.
There is some truth grain in the fact that rabbinic Judaism and rabbinic morals to some extent were influenced by greko-roman thought, although greek thought in itself was also influenced to some extent by the former as well, according to some greek historians and philosophers, but that may be questionable.
In any event, ethical writings of Judaism make for a small minority of Rabbinic and Jewish writing in the first place, thus here is the first absurdity in the notion that rabbinic Judaism began at that era.
It is true that Ethics of the Fathers, which is a small part of the mishna, is very very similar in its notions to greek ethics and the new testament, but it is most important to note that rabbinic judaism as well as modern judaism, "Ezraic" judaism and such are all primarily Legalistic doctrines, and thus are evidently rooted in a tradition other than the largely ceremonial/festive/contemplative/ethical grecko-roman-christian nature. And while it is also true that European Judaism in terms of morality was substantially influenced by Christianity, just as Iberian/Oriental Judaism was signficiantly influenced by Islam, the legal traditions are more or less the same, and the bulk - the part and parcel of what is considered Judaism, has remained relatively homogenous since well before the second temple at least. Unbroken chain since moses? subject to historical debate etc. but certainly much older than Christianity.
Regarding Jesus, however, the subject is a bit shady. Assuming that Jesus (1) existed, and (2) existed as he was portrayed in the New Testament as (3) interpreted by trinitarian and paulian christianity, would mean that he was primarily a rabbinic figure in terms of ethics, together with some essene influences (Revelation is a good example of this) would be considered a heretic, and of such Judaism would have a very negative view, not merely a "Nice Jewish Boy". The first reason simply being the fact that the New Testament is considered scripture in the first place, which is heretical.
As soon as one of the three qualifiers above is removed, the Jewish view of Jesus becomes more flexible.
Historically, all Jewish literature on this subject has unequivocally condemned Jesus by rather harsh terms, perhaps partly due to Christian persecution. On the other hand, we find some correspondence between Rabbinic sages and early Jewish Christians as well, suggesting that the Rabbinic view of early Christianity was not as solidified as it is now.
The "Innovation" of Jesus, if it can be called that -- and this is evident throughout the new testament, is the scorning of the law and the scholarly elite - or perhaps legalism and scholarism in the first place. Jesus felt he had the right to criticize the movement as he himself was a pharisee (as is quite evident from the gospel). However the big question in Judaism, and ultimately whether he is deemed to be a heretic or not - is whether he intended to abolish the law, or whether he attempted to appeal to those who were incapable of learning and following the law. Mind you, such sentiment is not original to Jesus, and you will find similar criticism in the Talmud and Mishna - although in the latter the criticism is mainly anecdotal and not thematic like the New Testament.
There is much more to write about this, e.g. the benefits of a legal religion altogether, or whether a "Humanistic" and "Moral" religion is preferred (I would like to note that the "Humanistic" and "Traditional" Reform Judaism is becoming more assimilated, whereas the Legalistic branches of Judaism remain strong and relatively unbroken in their traditions, per above.., the merits, the defficiencies etc. but I do not think the place is here)