The key theme of intolerance is shown through the innocence of the children and, as others have noted, is not limited to racial intolerance, but includes other social injustices too. Scout's success in breaking up the mob at the courthouse with her questioning of Mr Cunningham is effective because he sees her showing tolerance and appreciates that Atticus has respect for everyone and is an admirable man for this outlook. Mr Cunninghamis shamed in to accepting the views of others.
At least Jem and Scout are tolerant in the intolerant town of Maycomb. Atticus has done a good job in raising his children to not judge people based on rumors and racism. Jem and Scout will grow up to change society for the better. As one post mentioned above, it is a slow process to change the people of Maycomb, but change is forthcoming.
Intolerance is such a key concept in this important novel. We not only see this in the central plot of Tom Robinson's trial, but also in the way that Jem and Scout and the townspeople are intolerant of Boo Radley and the townspeople treat Atticus for trying to uphold justice. Intolerance therefore is a massive theme in this novel and one that is worthy of analysing further.
Remember that it's not just racial intolerance that is going on here. There is also class based intolerance. You have people like Aunt Alexandra who believe that somehow a person's "bloodlines" have a great deal to say about their quality as a person. This is a major aspect of intolerance and it splits the community almost as much as the racial intolerance does.
As others have noted, intolerance is perhaps the main theme of the book. Atticus's advice that in order to understand another person one must adopt, at least temporarily, that person's perspective (or metaphorically walk in his shoes) is one of the main messages of the book. Intolerance in the book leads to misunderstanding, pain, ostracism, isolation, stunted lives, and even death. Intolerance often causes the very same problems in the world in which we live.
Racism, social inequity and gender bias are just three of the problems that divided Maycomb in TKAM. Tom Robinson died because of the jury's refusal to give a black man a fair shake; Boo Radley decided that remaining inside his house was better than mixing with the townspeople who created lies about him; and Scout and Jem wondered if their father had any true friends in the town.
There is also more deep-seated intolerance seen in the novel which would take more than one grand trial to change. The long-held racist attitudes of white society against the blacks of the the community are seen throughout the novel. While it is evidently clear that Tom Robinson is not guilty of the crimes he is charged with, it is not yet possible for a white jury to find him not guilty. The old, intolerant attitude says that white people who accuse black people must be believed. The mere fact that the jury actually takes some time to debate the verdict is seen as a small victory for Atticus because in the past, the jury wouldn't have talked about it at all; it would have been an automatic guilty for any black defendant. The society isn't capable of full-blown change, but it is coming slowly. Too slow for the innocent Tom Robinson.
Intolerance was a main theme in the novel. The prejudice of the society, as a whole, tended to force the people to make snap decisions about those not like them. Therefore, the intolerance hurt the society based upon the fact that they would simply dismiss a person's worth based solely upon their race.
Intolerance forces people into needless arguments and difficulties. The townsfolk were intolerant of Boo Radley. His family was forced to keep him locked up at home and kept separate from everyone. It was a hardship for the entire Radley family and it separated all of them from the rest of the town. Mr. Ewell was intolerant of his daughter and of Tom Robinson. The reader knows that Tom didn't do anything wrong. He is convicted of a crime that he did not commit because the townsfolk were intolerant and prejudice. Intolerance can lead to many difficulties there is no real need for.
Injustice permeated the TKAM. The white citizenry in the town enjoyed the privileges afforded by their skin color; they certainly didn't suffer physically and financially because of racial tensions. But they suffered intellectually through the lens of racial prejudice.
And the blacks were subjected to many hardships all on account of their race.