From my reading of the Bible and New Testament, I don't think Christianity replaces anything. Nothing is replaced. There is no "Replacement Theology."
Jesus came into this world for purely sentimental purposes. It wasn't part of some Divine Constitutional Law. He wasn't following some system of rules or formal protocols. Actually, what he came to do was to nullify the moral authority of such a system of rules and formal protocols. In other words, his purpose was to do away with the Systematic Law so that we could align ourselves to something more natural -- something more sentimental -- the Natural Law.
He came as a liberator to emancipate us from ideology and dogma. He came to free us from what the Israelite religious leaders believed was the "Divine Constitutional Law." He freed us from this "Divine Constitutional Law" by proving that it never had any moral authority in the first place. He showed that it was invalid by allowing the religious leaders to condemn an innocent, righteous man -- himself.
Don't get the wrong idea, though. I'm not talking about Judaism here. I'm talking about man-made distortions of God's religion. Both Jews and Christians have done that for centuries. It's where religious leaders turn God's religion into a Constitution. It continues in today's world with the issue of abortion and gay marriages and the "Christian Right" movement in America. It's where people believe in a political system more than they believe in individuals. People's lives are enslaved by ideology and the structure of the world -- and they start believing that to make the world a better place they need to "re-structure" the world. The religious leaders in Jesus' day were doing something similar. Personally, I don't think changing rules and laws is going to help anyone. It doesn't make us better people.
In a sense, Christianity has no new theology at all. Christianity isn't about "changing the rules." It's just a story we believe in. It's a story of how a man died on our behalf to free us from formal protocols. The legacy of that man lives on. It's a shift in focus. Once upon a time we believed rules and formal protocols were the most important ingredient in "purity" and "righteousness." Then along came a man who changed all that . . .
The terms "Christian" and "Jew" are just a way of labelling people to distinguish who believes or does not believe in that story. Think of these two words as like a signpost. It's like we're fans of a Christian concept of Jesus. I don't see how it's wrong to be a fan. Fans of celebrities like John Farnham, Nicole Kidman, Greg Norman and Andre Agassi aren't bigots. Fans of celebrities devote themselves to the personality, charisma and life story of that person. It's like that with Christianity. It's a religion dedicated to the memory of a person.
It's about the story and legacy of one man. This story means something to us and we think it's important.

We're not going to throw this story in the dumpster just because it happened two thousand years ago. Moreover, if our religion is about a God we can trust and a personal connection with that God, then it is important that we recognise what such a God has done for us. Christianity is supposed to be something sentimental. Sure, there's a long history of disputes about what is correct or incorrect about the story and concept of Christ, but these are just attempts to forge something concrete and systematic in Christianity. It's where people try to fit Christianity into some kind of model, philosophy or mystical science.
The "bigotry" is a result of a belief not in something sentimental, but something systematic, scientific and concrete. It's a result of people trying to compartmentalise Christianity. It's where people do it with their heads and not their hearts. They believe Christianity should be compartmentalised and that these compartmentalisations apply to everybody.
It's when we realise that Christianity was meant to be something purely sentimental that we stop all the bickering and factionalism and realise that what we fought over wasn't what Christianity represented in the first place. It's just us trying to fit Christianity into some kind of model. When we focus on the sentimental we start connecting with people and we start appreciating the true meaning of the Religion of Christ, and accepting each other's differing views. We may even start realising that there is no real difference between the Religion of Christ and the Religion of Israel. The only significant difference is that the Religion of Christ is the story of what God did to reconnect with His people.
Christianity isn't a threat. It's an invitation. You don't have to come. Try thinking of us as more like a social club than a recruiting force.