First of all, Atticus respects everyone. He does not seem to see social class or race. He also treats both rude and kind people with respect. He teaches his children to do the same.
Atticus believes in standing up for people who have no voice. For example, in chapter 11 he describes his decision to take the Robinson case this way:
This case, Tom Robinson’s case, is something that goes to the essence of a man’s conscience—Scout, I couldn’t go to church and worship God if I didn’t try to help that man.”
He tells Scout that he did not just take the case because he was told to, which would make it not his fault, but because he felt it was the right thing to do. He feels like Tom needs him, and it is his ethical duty to help. He tries to explain to his daughter that he would not be an honest Christian if he didn't.
“They’re certainly entitled to think that, and they’re entitled to full respect for their opinions,” said Atticus, “but before I can live with other folks I’ve got to live with myself. The one thing that doesn’t abide by majority rule is a person’s conscience.” (chapter 11)
Atticus also teaches his children to respect everyone, including those who seem rude or grumpy. If they don't understand a person, he urges them to "climb into his skin and walk around in it” because "you never really understand a person until you consider things from his point of view" (chapter 3). He tries to get Scout and Jew to see people for who they really are, not who they appear to be.
Finally, Atticus teaches his children that people are not always what they seem. When Jem crushes Mrs. Dubose’s flowers, Atticus sends him back to apologize to her and she asks him to come back for a month to fix the flowers and read to her. He explains to Jem that Mrs. Dubose has been fighting a debilitating illness and trying to wean herself off morphine.
“I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. It’s when you know you’re licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won, all ninety-eight pounds of her. According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew.”
Thus, Atticus teaches his children to respect people, whether it’s popular or not, whether they are your equal or not, and whether you like them or not.