Atticus recognized a very important consequence of racism: It damages or even destroys the victim (as in Tom's case), but it destroys the character and the humanity of the victimizer. Aunt Alexandra obsessed about social classes, social status, and "fine families," judging little Walter Cunningham to be "trash" because of the circumstances of his birth. It is Atticus, however, who defines for his children (and for us) who the "trash" really is in society. Atticus says:
As you grow older, you'll see white men cheat black men every day of your life, but let me tell you something and don't you forget it--whenever a white man does that to a black man, no matter who he is, how rich he is, or how fine a family he comes from, that white man is trash.
Racism in any form is cheating. One message in the book is that a denying equality for someone else degrades the one who denies it.
Cadena did a marvelous job in answering this question, and covered most of what I could add. However, I do think another part of Lee's message about inequality is that inequality and racial feelings/attitudes can bring out the worst in people. Atticus mentioned that the Cunninghams were decently good people, but yet race caused them to organize a lynch mob and come after Tom Robinson at night.
Atticus also mentions that everyone goes stark raving mad whenever there's an issue involving a negro. During the depression era, most everyone in Maycomb was equally poor and unemployed. Very few, like Atticus, had steady employment. The only thing that people could hold onto in terms of social status was their notch on the racial totem pole, so to speak. People like Bob Ewell, who was dispicable and low down still felt a sense of superiority because they were White, even though there was nothing superior about them at all!
Here's some questions to consider as you think about this topic. Which characters in the book were the "good" guys? If you think about it, the answer will probably be Atticus, Calpurnia, and Boo Radley. And, who were the "bad" guys? The most obvious answer is Bob Ewell and possibly some of the men that gathered in the mob outside of the jailhouse. So, what made the good guys good? Well, they measured people by the content of their characters, or, how good of a person they were. And, they were good people themselves, regardless of their race, economic status, or social standing. Atticus was kind and fair to everyone, taking Tom's case even though it would lose; Calpurnia, though black and looked down on in their society as not being equal, taught Jem and Scout how to be decent, caring people; Boo Radley, though a social outcast and at one time a social misfit, made a heroic save in the end of the book, helping kids in a difficult situation. Then there is Tom, a hard-working black man with a family, who was trying to help Mayella, a white woman; was kind to her and tried his best to not hurt her feelings. So all of these people were good people, they had good characters, and did good things even when it was hard. On the other spectrum is Bob Ewell, who did what Atticus said was the most despicable thing a human being could do: take advantage of a black person's station in society to be unfair, cruel and discriminating. He was a liar, a hypocrite, a racist, and the least deserving of any sort of equal treatment in the book.
All of this seems to say that Harper Lee is saying that it isn't social class, race, or money that made people equal in this book; it was how they treated other people that made them equal or unequal. Atticus, Boo, and Calpurnia were equals because of their kind treatment of others; Bob Ewell was below them in respectability because he used people to cover his own weaknesses.
That is one route that you can go. I hope that those thoughts help get you started; good luck!
Harper Lee, Judging from her novel To Kill a Mockingbird, comes out very strong against discrimination between people because of inequality of any kind. It is very common for us to hear arguments discrimination based on group characteristics such as race, religion, social class, and sex. But Harper Lee, through the medium of Atticus is professing equal treatment of people regardless of their personal qualities, and actions.
Atticus is a very good at shooting, but he considers it wrong to consider himself superior than others because of this.