Jesus' message was, among other things, that it is a person's actions that count, not a person's social status. He rebuked the wealthy and the powerful while calling on people to help the poor. In this, he is like other Hebrew prophets before him. He also repeated the traditional Hebrew injunction to love one's neighbor. His innovation, however, was to teach that people besides other Jews could be your "neighbors," in contradiction to the traditional use of the phrase. For him and for those who believed his message, "neighbor" no longer meant "fellow Jew."
For example, the parable of the "good Samaritan" was about people being judged by their deeds, not by their ethnicity. The parable has practically lost its meaning to present-day audiences because we don't know any Samaritans other than "good Samaritans." For Jesus' audience, however, Samaritans were a rival ethnic group who worshiped God improperly. As non-Jews, they did not qualify as "neighbors." For an example of how much the Jews disliked the Samaritans, here's what the prophet Hosea had to say:
Samaria shall become desolate for she has rebelled against her God. They shall fall by the sword, their babies shall be dashed to pieces, and their pregnant women shall be ripped to shreds. [Hosea 13:16]
Yet Jesus challenged his listeners to consider the Samaritan as the true neighbor of the man beaten by robbers. A priest and a Levite, on the other hand, had left the injured man in the road.
Since modern readers don't bear any grudges against Samaritans, the parable doesn't mean to us what it meant to Jesus' audience. We'd have to rewrite the parable as "the good Iranian" or something like that. And even if we rewrote it thus, it wouldn't come as much of a surprise to our audience that an Iranian could be a good neighbor because we expect not to discount someone on the basis of their nationality or ethnic group. In fact, the reason the parable's meaning is lost on us is because of the parable itself. The reason we don't think of "neighbor" as "one of my people" is that Jesus (and Christians following his example) successfully challenged that way of thinking.
Since Jesus quoted Jewish scriptures, some have concluded that Jesus added nothing to them. See, for example, Clarence Darrow's "Absurdities of the Bible." In fact, Jesus reinterpreted scripture while quoting it, as the parable of the good Samaritan shows. Also, Jesus' Golden Rule replaced the less ambitious rule of scripture, which was that one should not do to others what is hateful to oneself.
After Jesus, Paul the Apostle took up the banner of equality across social strata or groups. We see this attitude most clearly in Paul's letter to the Galatians:
There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for you are all one in Christ Jesus. [Galatians 3:28]
Paul denies the special status of an ethnic group, saying that such status is a worldly phenomenon and that people are equal in God's eyes:
But glory, honor, and peace, to every man that works good, to the Jew first, and also to the Gentile: For there is no respect of persons with God. [Romans 2:11]
While it's true that the Christian churches in their various manifestations have proved less than universally effective at reigning in the human tendencies toward racism, nationalism, sexism, classism, and so on, it's also true that Jesus' message of human equality has endured.
The poison of the doctrine 'equal rights for all'—this has been more thoroughly sowed by Christianity than by anything else.
Nietzsche despised Christianity's message of equality and, in contrast, glorified Hinduism's caste system.
The US Declaration of Independence declared "All men are created equal." That statement owes its credibility in large part to Jesus' message of equality. Thomas Jefferson was so conscious his debt to Jesus that he collected Jesus' moral teachings into a book, The Life and Morals of Jesus of Nazareth.
PS: It's ironic that, despite his message of inclusion, Jesus is now used to define in-groups and out-groups.
Do Unto Others or Not: Another of Jesus' innovations
Jesus the Relativist: why his teaching is still relevant 2,000 years later.
Slavery and Relativism: Is it a coincidence that "Christendom" ended slavery across the globe?
Text of the Bible courtesy of Project Gutenberg