Here's Anne Lutz Fernandez on the epidemic of book banning, which is affecting not only schools and public libraries but even commercial bookstores and publishers. There are some complexities here which she doesn't really address, so I'll give it a try.
Obviously there can be legitimate debate about what books schoolchildren should be assigned to read, and also what should be available to them in the school library, although these are certainly not the same question. Assigned readings need to be age appropriate, and they need to include what is acceptable to a wide range of the community. Children are being made to read it and it seems that parents in principle have a right to object. That said, in my view and that of most people who share democratic and liberal values, they ought to be exposed to a range of ideas and viewpoints, including those of people their parents don't agree with, all the more so the older they get and the more capacity they have to think for themselves. We can debate what the limits of that range are, but it should include most of what is intellectually respectable and factually accurate. Finally, of course, what is available in the library should include material that you might not want to assign.
Public libraries of course hold a lot of material which is intended for adults, but I suppose the question of what material intended for children should be there isn't radically different from what should be in the school library,, and we can also debate what adult materials children of various ages should have access to. It's not so simple as "anybody who doesn't children to have uncontrolled access to some particular book in the school or public library is an enemy of freedom." I can certainly think of examples I would support.
But. In the first place, what you want for your children is not what everybody else wants. Giving every individual a veto over what is in the library is going to take away other people's rights and freedoms. Our cultural ideal of free speech means you're just going to have to put up with a whole lot of stuff you don't like. In the second place, it's important for that stuff you don't like to be there and be available, and you really ought to read it yourself. I've already said here many times how sick and tired I am of people yelling about communism who don't have the slightest idea what it means or what range of beliefs have come under that label. The same goes for fascism. Das Kapital and Mein Kampf are both in the library for good reason. There are many interpretations of history, and if you want to understand history in a sophisticated way you need to check out more than one. You can't legitimately decide that you don't like A People's History of the United States if you haven't read it.
In the third place, most of what people are trying to ban now is just books by and about non-white and gay people. That's it. People don't want their children to know what life is like for those people and that they are actually human. People also don't want their children to learn true and accurate history because they think it might disturb their children, or shatter some sort of unquestioning faith that they are supposed to have, even though it's based on fallacy.
Finally, I do believe that society needs to move on from some beliefs of the past which we now know to be false. The earth is about 4 1/2 billion years old. Life evolved over more than 3 million years, and we have a good understanding of how that happened. The wrath of God is not the cause of natural disasters. The history recounted in the Bible is largely fictitious. Race is a social construct, not a scientific reality. People do not choose to be gay, or transgender, it's just how they are. I could go on. The point is, there are facts that some people want to deny. Nope. You don't get to do that.