I think she is making the point that the educated have a better understanding of general diversity - and are therefore more responsible for tolerance.
Consider Atticus' lessons to Jem and Scout throughout the novel - all about walking in someone else's shoes... however, Atticus never presumes to explain that the Cunninghams or the Ewells or even the Robinsons need to do the same thing. Granted, he is responsible for raising his own children and not the entire town, but it is indirectly implied that because Atticus is a professional and more educated than most (and also offers this expectation to his children who learn to read at early ages), he is more responsible for having tolerance, teaching tolerance, and living "above reproach" than those who are less educated than he is.
Miss Maudie is also an example of this. She has a much keener knowledge of the inner workings of society, and she is also used throughout the novel as a teacher of tolerance. (Think about the Missionary Tea scene - Miss Maudie has this expectation of all the "educated" women in the room, but because they fail in the tolerance department they are presented as hypocrites, and therefore, actually ignorant.)
Lee is clearly saying that in a society, our level of respect for others is directly related to our intelligence. Those who are ignorant of others' differences cannot be held responsible for understanding and respecting those differences. Those who have understanding of the differences, must have the most respect.
In the same year that Harper Lee won a contract for her unfinished manuscript for To Kill a Mockingbird, Congress passed the Civil Rights Act of 1957. However, African-Americans did not see enforcement and protection of their rights until the Civil Rights acts of the mid-sixities. So, Harper Lee's themes of tolerance were extremely timely.
As the daughter herself of a prominent attorney, Lee was aware of the injustices in the South, especially. During the 1950s, women and blacks were excluded from juries and could be arrested, tried, and punished with little cause. Relevant to the Tom Robinson case is one that took place in 1955: Two white men were accused of the murder of Emmett Till, who allegedly harrassed a white woman. Like the trial of Till, the jury was made of twelve white men and the courtroom was segregated. In one hour, the men were acquitted.
Aware of the inequities in the South, Harper Lee set about to present moral lessons of tolerance. The concept of climbing into someone else's skin and walking around in it is one that Lee felt would help people to understand others. In fact, this concept is one with which she begins and ends the novel, bringing to light the various biases prevalent in people's minds about the members of their community is all social stratum. Harper Lee's message was timely, and avant-garde both.
In my opinion, she is trying to communicate the idea that all people are worthwhile and that we, as people, need to work to understand others so we can see how they are like us. If we look at things from their point of view, she says, we will be able to understand why they act the way that they do and we will be able to sympathize with them rather than looking down on them.
You can see that at numerous points in the book. Atticus and Calpurnia try very hard to instill this idea in the minds of the two kids.