How is Harper Lee approaching the topic of racism through Francis Hancock, Tom Robinson, and Dolphus Raymond in To Kill A Mockingbird?

Francis demonstrates the ignorance and cowardice of the town at large. He spews the hate that his family speaks without questioning it, telling Scout that Atticus is a "nigger-lover", & that he "lets you all run wild", referring to Jem and herself. He goads Scout into a fight, proving that racism often leads to violence. Overall, Francis is an individual who symbolizes the unthinking majority of people who accept others' viewpoints without judging for themselves. He employs no critical thinking, then hides behind his grandmother when Scout attempts to call him on it. Just like members of a mob, Francis has no spine when he's actually forced to confront his actions.

Dolphus Raymond is a local "drunk"; or at least, that's what everyone thinks. He is a white man from a good family, but he has chosen to live on the black side of town with his mistress, who is also black. There, they raise their children, & live in relative peace. He is a source of rumor & speculation amongst the townspeople, because of his chosen lifestyle. His secret? Mr. Raymond is not an alcoholic. In fact, all he carries in his brown paper sack is a bottle of Coca-cola. When Dill leaves the courtroom distressed, Mr. Raymond shares the soda with Dill, and talks with the children about tolerance and love. He explains that letting everyone think he's drunk helps them deal with the fact that he's chosen to ignore social standards, and instead pursue happiness with the woman he loves. He understands Dill's sickness at the cruelty he has witnessed during the trial, and explains that when they are grown, they'll no longer cry about the injustice in the world. Mr. Raymond is another adult, like Miss Maudie and Atticus, who teaches the children a lesson in equality, and extending compassion to all people.

Tom is the catalyst for the racism running deep beneath the town. Through his trial all the ugliness and secret hatred in the small town is brought to the surface.  He is a quiet, hardworking family man, whose existence stands as the ultimate symbol of the mockingbird in the novel. In fact, his only "crime" is being black. He was simply in the wrong place at the wrong time, & thus the sins of Bob Ewell were visited upon him. The town uses Tom as an example, a scapegoat for their own hideous bigotry. However, Atticus, and those who support him, show how racism can be fought. They make it clear that Tom is innocent, and that his trial is merely a showcase for the racism of the town.