This story takes place in the South after integration, but as the story reveals, racism is not something that can be easily erased from people's minds and hearts by legislation.
Many of Flannery O'Connor's stories, like this one, deal with racist themes and she has been criticized for using the "N" word and for her portrayal of blacks, but in her writings and essays, she explains that she was attempting to point out the evils of racism and how anti-Christian racism is. This particular story is loaded with irony and the biting nature of the irony points out the ugliness of the racism being criticized.
In this story of mother-son conflict, one of the many things the mother and son disagree on is race relations. The mother is prejudiced. She reminisces about her childhood in the plantation culture of the Old South where everyone knew his place. This irritates her son, Julian. She has refused to ride the bus since the buses have been integrated, and as soon as they board the bus, Julian sits near a black man to annoy his mother. He dreams about how she would react if he married a black woman. The mother wants to give a penny to a little black boy, and Julian repeatedly advises her not to do so. She is attempting to act in a benevolent way, but it is really condescending, and the boy's mother strikes her, knocks her down and she dies from a heart attack.
The way the mother talks with people on the bus and the condescending way she thinks she is doing the little boy a huge favor by giving him money shows how racism still exists, especially in the older generation. You can read the analysis of the short story here on eNotes.
As for the rest of your question, you have to compare racism to other works that YOU have read. If you read more of Flannery O'Connor, you can find a lot of examples of the legacy of racism. Have you read The Color Purple, or I Know Why the Caged Bird Sings or The Autobiography of Miss Jane Pittman, A Gathering of Old Men (or anything by Ernest J. Gaines, for that matter) - even The Adventures of Huckleberry Finn or The Adventures of Tom Sawyer or To Kill a Mockingbird? All of these works illustrate the ugliness of racism.