The town of Hillsboro, Tennessee is on trial in the sense that the beliefs of the townspeople regarding the truth of evolution or the truth of creation as told in the Bible are being debated and judged.
The banner over Main Street declares, "Read Your Bible" and establishes the position of most of the residents as believers in the Biblical creation story. The suggestion that man was not created by God in a single act, but grew and evolved from monkeys was offensive heresy and an affront to the good citizens and their beliefs.
The few individuals in town who sympathize with Bert Cates and consider evolution as a factual phenomena vary from arguing their beliefs to working to support Bert to poking fun at the other side. Consider Howard and Melinda's discussion in the first scene.
Howard: What’re yuh skeered of? You was a worm once!
Melinda: (Shocked) I wasn’t neither.
Howard: You was so! When the whole world was covered with water, there was nothin’ but worms and blobs of jelly. And you and your whole family was worms!
Howard's intent was to make fun of Melinda. But for many others in town, the intent was to try, judge, convict, and punish Bert for threatening the beliefs of the townspeople.