As a Southern lady, Aunt Alexandra's racial prejudice is more subtle than that of others in Maycomb since it is connected to her social level of society as well as with race.
Alexandra's haughtiness and disdain extends to "white trash" (e.g., she frowns on Scout's desire to have Walter Cunningham come "home to dinner" in Chapter 23) as well as the "Negroes." So, when she expresses her distaste with the children's having attended Calpurnia's church, there are elements both of class and racial bias. She believes that such behavior is "just not done" by a Finch.
Likewise, when Atticus takes the job of defender for Tom Robinson, Alexandra views this task as somewhat below the status of an accomplished lawyer and member of the political set of Alabama. She also it distasteful for a Southern gentleman to be involved with the dealings of Negroes. She asks Atticus if there is any way he can avoid this assignment.
Aunt Alexandra demonstrates prejudice in To Kill a Mockingbird by the racist things Francis repeats her saying about Atticus.
Aunt Alexandra is Atticus's brother. Scout considers her hard and heartless, and does not like her much. However, at Christmastime we learn the truth about Alexandra and who she really is.
We learn the extent of Aunt Alexandra’s prejudice when Scout’s cousin Francis tells her what Alexandra (his grandmother) said about her father’s defense of Tom Robinson.
Grandma says it's bad enough he lets you all run wild, but now he's turned out a nigger-lover we'll never be able to walk the streets of Maycomb agin. He's ruinin' the family, that's what he's doin'." (ch 9)
As a Southerner, Alexandra has common prejudices. Yet Atticus’s actions demonstrate that not everyone in the area is racist. Her comments about Atticus are an insult to her brother and demonstrate the negative aspects of her character.
Many people disagree with Atticus's decision to defend Tom Robinson, and many townspeople have called him the same name. Alexandra's comments about him ruining the family greatly upset Scout, and this is why she fights Francis. When she gets in trouble with Uncle Jack, she tells him why. He is just as angry, and realizes how much damage the trial is doing to the family.