Alexandra's view is that class and culture are essentially identical and also are deteminant of personal quality. She is concerned with social status and the perception of her family (and family name).
Atticus, alternatively, feels that personal quality is determined otherwise. His character seems to imply that people are not only "good despite their circumstances" but essentially good by nature. He is concerned for doing the right thing and not concerned, primarily anyway, with perception.
The Cunningham's are poor, but they are a respectable poor. This contrasts with the Ewells. Trash is not a good way to describe people, but if ever people were to be described as trash, it is them. Atticus believes that people are people, and Alexandra believes that some people are better than working than others.
It is hard to believe that brothers and sisters could be so different. Scout had her own hypothesis about Alexandra.
... when Jem told me about changelings and siblings, I decided that she had been swapped at birth, that my grandparents had perhaps received a Crawford instead of a Finch.
Despite Alexandra's high-handed opinion about her family upbringing and the need for her to provide motherly guidance for Scout, she has a poor track record. Her son, Henry, "left home as soon as was humanly possible, married and produced Francis." Aside from Bob Ewell (and his chip off the block, Burris), Francis is the most detestable character in the novel, and Alexandra apparently pampers him during his visits to Finch's Landing.
As for the Cunninghams, they would probably be considered "poor white trash" in many areas of the South. However, the Ewells have a stranglehold on this distinction in Maycomb, so the Cunninghams seem like "plain folks" in comparison. However, the Cunninghams are moonshiners who attempted to lynch Tom Robinson, so they are not among Maycomb's finest citizens--just not in the same class as Bob Ewell.
Alexandra is a snob. She thinks that people are who they are because of "blood." That means she thinks some people are better than others just because of their family background. To Atticus, you are good or bad because of your attitudes and your behaviors, not because of who your relatives are.