In a sense, Ray Bradbury's Fahrenheit 451 is a story where political correctness has been taken to an extreme. It's not so much about avoiding difficult topics, it's about keeping everyone happy; that means getting rid of everything that makes people unhappy. If Beatty's explanation is to be believed, censorship did not come from the government, but rather the people themselves. Though it is an extreme example, it mirrors aspects of today's society, particularly when it comes to online outrage.
Beatty's full explanation brings up the idea of keeping everyone happy:
Now let's take up the minorities in our civilization, shall we? Bigger the population, the more minorities. Don't step on the toes of the dog lovers, the cat lovers, doctors, lawyers, merchants, chiefs, Mormons, Baptists, Unitarians, second-generation Chinese, Swedes, Italians, Germans, Texans, Brooklynites, Irishmen, people from Oregon or Mexico. The people in this book, this play, this TV serial are not meant to represent any actual painters, cartographers, mechanics anywhere.
Here, the term "minority" does not have quite the same political meaning as it has today. Rather, Bradbury uses it as a way of showing how many different groups are found in the world. By this definition, "minorities" can be found in all shapes and forms, from cultures to various subcultures. If you look at the news or any social media platform, there seem to be numerous groups unhappy with controversial events and others's responses to them. Political divides and tensions result in strong responses and ensuing arguments between individuals and groups.
While it is hard to imagine living in a world where houses—and people—are burned for possessing books, it is easier to see how the society in Fahrenheit 451 may have come to that point. Eventually, rifts resulted in a demand to try to make everyone happy. The only way to do this, from Beatty's explanation, was to remove any source of conflict or controversy:
We must all be alike. Not everyone born free and equal, as the Constitution says, but everyone made equal. Each man the image of every other; then all are happy, for there are no mountains to make them cower, to judge themselves against.
For further study into this idea of parallels between today's society and Bradbury's novel, you might look at Mildred's obsession with television and how it mirrors current fascination with reality TV. Additionally, though it's certainly not the same as burning books, there is also a current trend of trying to shut down opposing viewpoints online.