What effect does the setting have on Fahrenheit 451?

Good question!
Setting affects Fahrenheit 451 in several different ways, all of which are important.
The first of these is that the novel is set in the future. This aspect of the setting is essential for the novel, since it is a warning about a possible (horrible) future, one Bradbury clearly wants readers to avoid. Many of the technological advances described in the novel were just getting started when Bradbury published his classic novel.
The second aspect of setting that affects the novel is the specific work setting of Guy Montag in the firehouse. It blends the fellowship of a friendly work environment with a traumatically alien reality: these firemen sit around playing cards waiting to burn books. They don't save lives. They kill animals there in the firehouse, for fun.
The third aspect of setting that plays a major role is domestic. The fires these men set are not in a public place, or some industrial setting, where they might seem natural, or at least acceptable. They invade people's homes in order to burn their books.
And the final aspect of setting playing a major role is nature. The smells of rain and plants Montag experiences with Clarisse are the intense opposite of the technologized home in which the Montags live.