As someone who works in a library, as long as speakers follow the policies - which mainly focus on being non-profit, etc. - they are allowed to speak. As for the books, libraries order books based on what is popular, what is educational, and what is wanted by the area a particular branch is in.

The intention behind this is to ensure everyone has access to as much information as possible, regardless of what side it's on. Libraries are a place for people to get unhindered access to information and resources.

As my coworkers and I like to say, "A library should have something in it to offend everyone." It's a silly way of saying, we don't ban books and we don't limit access to books. Any books, from any author. To do so would go against everything we stand for.

As for shelving the terf books in the LGBTQ section, that may have more to do with the Dewey Decimal code of those books than it does with personal librarian choice. If its code is 547.6, it'll go with other 547.6 books, for example, regardless of the point it is making.