Give an example from To Kill a Mockingbird of Atticus's understanding of his neighbors' beliefs while defending his own principles against them?

Another good example of Atticus showing understanding but
defending his own principles would be with the Ewells.  Atticus explains to Jem that
although it's illegal, Bob Ewell is "allowed" to hunt out of season.  He said that it's
illegal and should not be tolerated; however, knowing that he spends what money he does
get on alcohol, how could anyone deny his children the only meat that can be afforded to
appear on their plates. 

Because of Atticus' defending of
Tom Robinson, the kids start having issues with various people, which generally resulted
in fights.  In the conversation he had with Scout, he tried to explain to her that
things were going to get worse before they got better, and she needed to ignore the
ignorance of the people trying to get her upset, for reacting was just feeding their
actions.  He tried to explaining to her why people feel and react they way they do to a
white man defending a black man, but at the same time, making sure she understands that
people should always do what's right, regardless of the background of the person they're
helping or defending.

For Jem, the thorn in his side was
Mrs. Dubose.  Every time they'd walk past her house, she'd shout horrible things about
Atticus.  Atticus explained that she was just an old woman set in her ways, and that
regardless of what she said, it wasn't worth getting upset over because everyone was 
entitled to their own opinions.  At the same time, he argued that her words were just
her opinion, and opinion doesn't make them fact or truth.  Atticus taught the kids,
however, to speak respectfully to everyone, regardless of their beliefs, even though he
defended Mrs. Dubose's actions.