Public Libraries are treasures for a variety of reasons, and one of the most important is access to information. It is a rare instance that what you need or are looking for, can't be found in some way. Sure, the book might be out, or only available at another library, or the information is only accessible online, but it's here.
More importantly is that the information is either available in a neutral way, or there are books and information from all sides of an issue - to ensure a balance. In that way, if you are devoutly religious, we have books written that embrace that viewpoint. If you aren't, but interested in the topic, we have books written in a more secular manner. This is true across the board. That is the very basis of librarianship.
There are times that someone may feel that the balance is off to one side or the other, but people evaluate the world around through a lens that is shaded by personal outlook. It may not be a book to book balance, but a variety of points of view are carefully included.
In a broader sense, libraries should be open to anyone and everyone in the public. It is a public space. At the same time, it isn't a space for free-for-all behavior. Everyone needs to be mindful of others around them, and ensure that they do their part to welcome and not offend. Staff here works hard to make sure that services is equal to all under the policies in place. The Trustees work hard to make sure that the policies are fair with expectations that services and usage is similar no matter who you are.
A public library is a microcosm of our country, founded as it was as a refuge, and developed as a melting pot for people from around the world. The library is open to all that really want to make use of what it has to offer, and welcomes an amazing mix of people. We all have a part in making the library a positive experience for everyone.