Racism and the mad dog could seem unrelated, but as with most circumstances in To Kill a Mockingbird, it is all a matter of perspective.
The mad dog could function as a symbol of racism. As the mad dog begins to come up the street, people who know it is coming lock themselves in their homes, only to watch it suffer until death. They are afraid of what it could possibly do. Even after it's death Atticus tells the children to stay away because it is still harmful. Those who find the mad dog make sure to get the appropriate authority there to destroy it.
The white people of the society treated blacks the same way. They were afraid of Negroes. They were afraid of the black influence in their society. They were happy to watch them suffer. Racism also leaves a mark well after it is gone.
the dog is ment to signify racism coming towards the twn. all the neighbours shut themselves up to show that they are enveloped by it and keep there heads down. However, atticus stands up and shots the dog signifing that he has killed racism and will oppose it. you could say it was showing that atticus will try to fight racism for the rest of his life.
Also, calpunias son (is black) has to clean the dog, so it shows what kind of derogatory jobs racism creates for the blacks. And the son also tells the children to not go near it because its dangerous, so he cares about them even though racism is there.