Fahrenheit 451 is a Modernist work. It's considered a Modernist work because a battle of inner self vs. outer self takes place, the government is corrupt, and the rules are broken.
The battle of inner self vs. outer self begins when Montag meets Clarisse. She tells him that there is more to life and that he is different than others. Montag then begins to wonder why books were so important to people and ends up snatching a book without anyone knowing. He then has to keep this a secret and be on high alert. Throughout the novel Montag battles with himself, for example, after he killed Beatty he realized that he shouldn't have done it because it was what Beatty wanted all along. Another battle he fought with himself was when he questioned whether or not he missed his wife Mildred when she died.
The fact that the government was corrupt also made this a Modernist work. Things such as the parlor walls and the seashells were put out by the government to distract the public and make them not worry about what they were doing. The government also made laws to prevent the public from owning books because it would make them think, and the government did not want people doing that. Perhaps the most extreme example of the government's corruptness came when the police made the mechanical hound take down an innocent person so that nobody would know that Montag escaped.
During the Modernist period rules were broken. The very first thing that the novel says is, "If they give you ruled paper, write the other way." That quote basically says to not follow the crowd, be different. It foreshadows that rules will be broken later in the novel. Montag does break the rules and keeps a collection of books even though it's against the law. He pays the price for breaking the rules at first, but in the end he gets what he wanted.
In conclusion, Modernism was a time period where people broke rules, had a corrupt government, and battled their inner selves vs. their outer selves. Fahrenheit 451 includes all of these things and therefore makes it a Modernist work.