What are some of the fears being shown?
I think one of the biggest fears demonstrated in the novel was a prominent fear for this time period in America's history - this is the fear of things that are different.
No only is the book full of racism - but there is prejudice in general for all things different. Consider everyone who is gossiped about, avoided, and unfairly judged outside of the black characters. First, there is Boo Radley (and the Radley family). They are considered "weird" because they are not social - they don't serve lemonade on their porch on Sunday afternoons. Therefore, something bad must be going on inside that house. Then, there's Dolphus Raymond - who is a landowner and should be highly respected in the town, but because of the lifestyle he chooses (to live among black people like equals) he must pretend to be the town drunk. Also, there are the people who are looked down upon because of class distinction. Certainly the Ewells, who are considered "trash" - do not receive any respect. They aren't even made to follow societal "rules" like keeping their kids in school. The Cunninghams, though honest farmers, are treated differently than the children of the professional class. Atticus shows Mr. Cunningham respect and patience - but he is one of a few - evidenced by Mr. Cunningham's quiet and unobtrusive ways around town.
There is a general air of intolerance in the town - and not necessarily intolerance for things that are wrong - only things that are different. This intolerance stems directly from fear. Even in the educated and somewhat tolerant Finch household, Aunt Alexandria is furious about the fact that Calpurnia took the children to her church. Even Alexandria is, to an extent, afraid of things she does not understand.
Though it is only slightly different than the previous answer, one of the other major fears is that of the unkown. It is manifested in the actions of Scout and Jem as they perpetuate the town's attitude towards Boo Radley, but their fear is eventually resolved as they learn the ways that Boo is reaching out to them and the way that he defends them when they need it most.
There is also the fear of the unknown as it applies, like the previous poster wrote, of the different. There is an absolute unwillingness to allow for the differences in the town to be washed away, whites and blacks cannot mix, you even have the women gathering to send food to Africa but not be willing to consider the needs of the African Americans in their midst.