Burning books used to be a form of censorship. Back in the Middle Ages, for example, when books were rare, you could actually knock out all traces of existence of any given work of literature. Sappho, for example, is mostly unknown to us, except in fragments that survived. Back then, a book and the content it held were one and the same: burn enough books, you can destroy the content.
That isn’t the case anymore, in the digital age. You can burn as many copies as you like of any given book and they can still make more. In that light, burning a book becomes, itself, a form of symbolic speech, just like burning a flag. Symbolic speech is protected speech.
Don’t get me wrong. Chances are, whenever a book is burned, I personally probably disagree with the message that that book-burner is trying to propagate. But I believe they have a right to propagate it. Even by burning books. Maybe especially “holy” books. But don’t get me started on religion.