This is actually a very good question. The Christian church has, by and large, been doing theology that has largely robbed Jesus and the New Testament writers of their Jewish heritage. The over-reaction by Martin Luther and others during the reformation complicated things even more.
Recent scholarship (over the past 50 years or so) has been re-evaluating the New Testament by putting back in their Jewish context and it's birthed a view some have called "The New Perspective on Paul".
The short version is this: The Jews always believed that it was God's grace that saved them as a special people. The commandments and ceremonial laws were expressions of obedience to the one that had already saved them. The Jews never saw God as a cosmic scorekeeper that was tallying up goodness points to people could earn their way into the new world (notice I didn't say heaven. More on this in a sec). So when you read Paul and look at him compare grace and works, he's actually talking about all of those ceremonial laws that make someone Jewish. Paul teaches that through the Messiah, the grace of God has been opened up to all people - all people can become Abraham's children. It's not all the ceremonial stuff that makes one a descendant of Abraham, but the Grace of God and his faithfulness to uphold his promises. It was always faith that made it happen (Again, this is according to the New Perspective on Paul.)
Usually all of this is framed up in a conversation about who goes "Up" and who goes "Down" when they die. Throughout most of Hebrew Bible, the concern was that their people would enter the promised land "flowing with milk and honey" as promised to their ancestors. As history progressed, we see an increasing expectation that this promise would see its fulfillment as a restoration of Israel and the toppling of other governments. This reached a fever pitch during the inter-testamental times including several revolts of would-be Messiah's that would come and topple Rome/Babylon. This explains the hype around John the Baptist's message and surrounding the arrival of Jesus. While there were still many ideas of what salvation actually was, you really don't see it captured in "up" or "down" ideas all that much. Sure, there was a view that you "slept" along with ancestors and there were concepts of "the pit" but they weren't framed up the way we see them framed up in medieval times forward. The primary idea of salvation in the New Testament is that God has expanded his grace to include all nations (as promised in the OT) and that Jesus was the eschatological messiah that would put an end to the current, fallen, evil age and usher in the kingdom of God.
Here's the issue: some Jews did not believe that he was the Messiah, but some did. Those that did, followed Jesus expecting that at some point they would take up swords with him to finish the job. Nobody expected him to die - nobody. At that point, even those that followed him dropped their swords and went home. It was over.
As Christians believe, when the empty tomb was discovered and Jesus appeared to them, he was confirmed as Messiah and suddenly gained a new paradigm on virtually everything. They suddenly realized that the kingdom of God about Jesus toppling earthly governments but was about toppling the principalities and powers - "the Satan". (I could go on, but it would be helpful to study inaugurated eschatology to understand this view more).
Christians began to teach that the grace of God is available to the whole world and through the faithfulness of Messiah, all are welcome into God's family. Salvation comes as we share in his resurrection at the end of the age when this present evil age is destroyed and the new heavens and the new earth are joined together. It's not an 'up' or 'down' paradigm, but a 'move forward into' or 'get thrown in the garbage' paradigm.
Helpful books (that can explain this much better than I): Paul and Palestinian Judaism by E.P. Sanders, Paul in Fresh Perspective by N.T. Wright, The Day the Revolution Began by N.T. Wright).
Why are there still so many very devout, well-versed Jews? I'm no expert on Judaism, but it would seem reasonable to speculate that they do not believe that Jesus was the Messiah and interpret the Christian proof-texts differently. They also do not share in the new paradigm that came from the resurrection and therefore do not share in the re-interpretation of many of the Old Testament texts.