I think that the society in which Montag lives strives for social stability. The fact that books are seen as dangerous indicates that this is an order predicated upon stasis and consensus as opposed to dissent and change. Any fear of books and their suppression reflects a social order that seeks stability and a desire to preserve the status quo so that there will be no change at all. Yet, I don’t think that this is what ends up happening in the social order. The stability is more short lived than anything else. If individuals such as Montag, who are originally indoctrinated into the ways of the social order, seek to rebel against it, there is not much stability there. In the end, I think that the desire to cut off options and opportunities from its citizens reflects a desire for social stability. Yet, this is a short lived and temporary condition because it is not one where there will be much in way of dissension and fragmentation, one where there is more instability than stability.
I think one of the main points of this book is to paint a drastic alternative to our current society where freedom, intelligence and a sense of ambition live and flourish. Bradbury wanted to show what it might look like if society ever became as apathetic as it is in the novel.
While the novel may be science fiction, and therefore, certain ideas are sheer speculation combined with Bradbury's genius world of make-believe, one thing that is certainly true about the characters in the novel is that they are still humans. And Bradbury shows through his protagonist that the human condition (with its natural desire for personal freedom, intelligence, ambition, personal relationships) is still alive within them--it has just been suppressed and buried so long, most people don't recognize what it is. Enter Clarrise. Her role is to stir up the questions and emotions that Montag has already grappled with (slightly) on his own.
Through this microscope on Montag's life, we are not to assume that Montag is unique. Based on Montag's story--is this society stable? Certainly not. He is lonely. He comes home perplexed by a neighbor who causes him to rethink questions he's always considered a little dangerous. His own wife is also lonely. She has attempted suicide when he enters the house--and when she doesn't remember it, he makes it out to be something it wasn't. The firemen at the station do not really interact with each other on a personal basis and they rely on a robot to do their dirty work for them. But who is to say any of them aren't also dealing internally with the same questions as Montag?
So the world isn't changing much on the outside. That doesn't mean individuals aren't changing on the inside. This is a society that is largely in denial and has turned somewhat numb. But this does not constitute stability.
I think that you could argue this both ways.
You could say that they do have social stability. After all (if what Beatty says is true) they have been dumbing down their society since the time of the Civil War. That's a long time and that must mean that their society is relatively stable (to go that long without really changing). We also don't see any evidence of a major rebellion against the society.
But you could say they don't. You have people like Millie and her friends who don't seem all that stable. If your people are that messed up, is your society stable? And you still have the firemen being called to burn books. This implies that there must be a lot of people who still have books. This means that there is an undercurrent of unhappiness with the society.
So I think there is evidence both ways. What do you think?