Just the fact that Atticus accepts the assignment to defend Tom Robinson is an example of standing up for racial equality. Unlike most of his southern counterparts in the novel, Atticus does not just accept the case; he actually does a thorough job of investigating and defending Tom.
He listens to and believes Tom's version of events. Atticus realizes before he starts that he isn't going to win the case, but he does it anyway. He accepts the case even though it further alienates him from people in the town, infuriates his sister, and puts the lives of his children in danger. Atticus tries to explain this to Scout when he says, "before I can live with other folks, I've got to live with myself." He not only wants to set an example of how to treat human beings for his children and the people of Maycomb, but he knows that he must do the right thing.
At one point Scout and Jem are being teased at school for his involvement in the trial. One of the school children calls her a "nigger-lover." Scout does not even know what the word means, and has to ask Atticus about it later. This is further evidence that he is raising his children without the hateful labels that were so common in the south at the time. Furthermore, instead of being offended by the label, he proudly acknowledges it when he says, "I most certainly am. I do my best to love everybody."