What is the fundamental difference in Atticus’s and Alexandra’s views? Are the Cunninghams trash?
It is clear, from Atticus's and Scout's explanation of the social hierarchy in Maycomb, that the Cunninhams are a poor but proud family. As Walter Sr. is a farmer, and as farmers were hit particularly hard during the Great Depression, Walter is unable to pay Atticus with cash--so he pays him with food he has grown. Likewise, Walter Jr. has learned that he should never take anything that he can't repay, and as a 6-year-old, he has enough discipline to not accept lunch money from Ms. Caroline--even though he is hungry.
While reasonable readers see the Cunninghams as good people, Aunt Alexandra, who is primarily concerned with appearances, is only able to see their lack of money and education. It is clear, as the novel progresses, that Atticus and Alexandra don't agree on the importance of appearances. Obviously, Atticus values people for their inherent goodness, not their color, finances, or education.
The basic difference between Aunt Alexandria's and Atticus's views are that Alexandria represents the status quo for Alabama in the 1930s while Atticus is avant-garde, so to speak. That is, he is a 1960s man living in the 1930s. After all, for a Southern white man living in the Heart of Dixie during Jim Crow to profess that all people are basically equal would be virtually unheard of.
That Harper Lee places a man who represents the contemporary thinking of her environment at the time she wrote "To Kill a Mockingbird" (New York in the 1960s) and place him in her childhood world of South Alabama in the 1930s sets up the tension of her novel. Having placed this modern man in the Old South, Atticus's views receive grateful acceptance and rejection by the various types of people in the Main Street of Maycomb. Aunt Alexandria is simply one of these types: the Southern, genteel lady who socializes with the "right people," and whose charity is directed where it can be harmless and not disturb the status quo. She is a foil to the Civil Rights Era man, Atticus Finch, as are her ideas.
As part of his more liberal thinking, Atticus does not judge people by their socio-economic class as does Aunt Alexandria. Instead, he judges people on an individual basis--a concept heralded by Martin Luther King in the Civil Rights Movement. This attitude of Atticus also makes him an anachronism for the 1930s in the South.
Alexandra is very class conscious. She judges people by their family names, how long their families have lived in the South, and to which social class that family has always belonged. In her view, the old families in the South who owned land and enjoyed money are socially superior to other people. These families were, of course, all white. She is very proud of the Finch name and the history of the Finch family in Maycomb County.
Atticus rejects this notion of "fine families." He judges people on their character, not their family pedigree--when he judges them at all, which occurs almost never. Atticus is not interested in class divisions. He values honesty, hard work, fairness, and compassion.
Alexandra considers the Cunninghams, even little Walter Cunningham, as being "trash" because they are poor and uneducated. They lack the family background she sees as necessary for a family to be respectable. In her prejudice, she cannot see that the Walter Cunningham is a proud, hardworking, honest man who pays his bills and keeps his word. Little Walter is a sweet boy whom Scout wants to befriend because of his character and his nature; his poverty means nothing to her. Atticus and Scout don't labor under the generations of prejudice that inform Alexandra's view of her small world and other people.
I second most of Ms. Hurn's points. Atticus judges each man individually, while his sister is more concerned with their family backgrounds. While the Ewell's are quintessential "white trash," the Cunninghams are poor, hard-luck, working-class Southerners--a distinction that many people overlook.