The fact that Boolie intervenes and actually creates their relationship may represent the fact that blacks and whites during that time were forced to interact with each other. Hoke is definitely at a disadvantage at the start because society has deprived him of opportunities he cannot even read. It is ironic that she is a white Jewish woman, and he is a black man, yet they are both elderly and have experienced the harsh past when people of each of their cultures were wrongfully victimized.
Even though Miss Daisy claims she is not prejudice, society has shaped her mentality into subconsciously thinking that whites are above blacks. She blindly acts on this prejudice thoroughly the movie until there is a shift along with the civil rights movement which leads to a progressive change. For example, she never allows Hoke to accompany her to the places she has him drive her to. This is exemplified especially at the Martin Luther King dinner when she has an extra ticket, and thinks its a silly idea for him to go with her, yet she ignorantly claims she likes the change thats happening.
Another example of their character juxtaposition is when the temple is bombed. He presents a story of his that relates to prejudiced crime and violence, yet she refuses to acknowledge that they relate as victims during that time period. Through out time, their juxtaposed roles begin to shift to mutual respect and friendship. When Miss Daisy starts to develop a mental illness, her and Hoke seem to be on the same level while he is even at an advantage.
This is shown symbolically when she is sitting holding his hand and he is standing above her. Miss Daisy is older and is disabled, and he is younger, able to walk, and even has to feed her. Because this is the closing scene, it shows a final equality among the two which also reflects what was going on during that time period. People were starting to get over racism and the efforts of radicals like MLKJ were beginning to show in the development of society.