In To Kill a Mockingbird how are Jem and Dill affected by racism?

Jem and Dill are shocked and disillusioned by the way Tom Robinson is treated during the trial. First, Dill becomes emotionally overwhelmed by the way Mr. Gilmer, the prosecuting attorney, speaks so condescendingly and disrespectfully to Tom. He becomes so upset that he cries during the trial; so Jem has Scout take Dill outside to calm down. Once they get outside, Scout tries to explain that attorneys have to talk that way because that is their job. Scout even says something very insensitive: "Well, Dill, after all he's just a Negro." This shows that Scout does not have the mature perspective that Dill has, yet. Dill responds to her by saying the following:

"I don't care one speck. It ain't right, somehow it ain't right to do 'em that way. Hasn't anybody got any business talkin' like that--it just makes me sick" (199).

Clearly, Dill understands the nastiness behind the way Mr. Gilmer was speaking to Tom Robinson, but he can't articulate it. Dill feels great empathy for Tom because of the racism and prejudice being displayed. He is sickened and cries because of how much it frustrates him to see Tom treated so poorly. 

Jem, on the other hand, understands the ways of attorneys and trials; so, he puts up with Mr. Gilmer's attitude for longer than Dill can. With faith in the justice system, and in Atticus's arguments for the defense, Jem holds onto hope for Tom's acquittal up until the disappointing verdict is read. This is when Jem breaks down and cries. Atticus does his best to explain the nature of racism afterwards--although he doesn't use that word. He tells Jem that a jury of white men simply could not acquit Tom because of a long-standing tradition of prejudice and racism in the South. Jem has such a difficult time accepting this that he never wants to talk about the trial again. For example, when Scout wants to understand the difference between how Hitler treats Jews and the way her teacher, Miss Gates, spoke about African Americans after the trial, Jem explodes as follows:

"Jem was suddenly furious. He leaped off the bed, grabbed me by the collar and shook me. 'I never wanta hear about that courthouse again, ever, ever, you hear me? You hear me? Don't you ever say one word to me about it again, you hear? Now go on!'" (247).

Even months after the trial, Jem still isn't ready to face the facts of racism and prejudice--or at least he can't talk about them.