The answer to this question depends upon what one believes about the nature of man. Is mankind naturally good or evil? If he is naturally good, then one could argue that when men gather together and form a society, evil can result. If a person believes that man is basically evil, born into a corrupted world, then the answer to your question is both; for what makes up a society--a group of individuals. It is easy for someone to say that man is basically good and that society corrupts him, but then one must ask where the evil came from in the first place to corrupt the individuals who make up the "evil" society.
In regards to Bradbury, he often portrays the individual as good. The good individual must fight against the corrupt society/government. For the author, sometimes "good" simply means not conforming to society and remaining individualistic.
In F451 the society seems more desensitized and ignorant than evil. Hence, ignorance has led them to become desensitized and careless. They would be evil if they had the access to the knowledge and, with knowledge backing them up, they still made decisions with the intention of breaking rules and canons of society. Maybe we could use this to create an axiom that the biggest problem with ignorance is that it opens the door to evil-like behaviors based on the lack of information on the basics of anything.
Since a society is made up of individuals, then it seems that the individual is what makes the society in "Fahrenheit 451" evil. The people that make up the society in the story allowed their world to become what it is. Beatty explains in part I how the society came to be: the world became crowded due to population and the media with its eyes and ears everywhere; people wanted information quickly and efficiently; all the "frills" of a story removed and stories reduced to just the simplest form; stories without "frills" and reduced become boring and no one wants to read, people unhappy with anything that is considered offensive so all possibly offensive material is removed in the name of political correctness; anything that makes people think and analyze is too much work which again makes people unhappy so thought-provoking material is removed; everything is about having fun right now, including school. Reading stories caused people to think, thinking caused people to evaluate their world and their lives, and that evaluation caused people to want to make changes. To eliminate that chain of events the first item in the chain - reading books - was eliminated in the society of the story. People allowed themselves to become lazy and self-indulgent to the detriment of themselves and their society. It all began with the individual.
Since society is made up of individuals, it is individuals to blame. You can't blame all Germans for the atrocities of WW II. While it might be true that many looked the other way, only the responsible people should be prosecuted, and if looking away is a crime, then they should be held responsible too.
It would be a mistake to brand any complete society as evil. Yes, societies do develop characteristics that are unjust to some people within or outside the society. But that does not make everything about society as evil. For example, America practiced slavery till 1865. By no stretch we can justify the practice of slavery today. But this does not mean that American society was an evil society.
Many a times social practices that were accepted and perhaps even good, become unacceptable and harmful with changing time. Societies take some time to discard outdated bad practices and adopt new required practices. Because every society, at any point has some bad things that need to be changed. Presence of these bad aspects of a society should not be used as an excuse to brand the everything about the society as evil.
Some people within a society can be intentionally evil. But it is not possible that every person within a large society is evil. It is important to note that behaviour of individuals is very much influences by the culture of the society, so we must differentiate between wrong doings of individuals due to evil intentions and cultural pressure.