The primary argument supporting a claimed First Amendment prohibition on public libraries' excluding books based on viewpoint was the First Amendment right of listeners. The majority in today's Little v. Llano County en banc decision held that this right doesn't give people an entitlement to have the government provide the materials in the library:
We hold that plaintiffs cannot invoke the right to receive information to challenge the library's removal of the challenged books.
First, plaintiffs would stretch the right far beyond its roots. As discussed, the [Supreme Court's right-to-receive-information precedents] teach that people have some right to receive information from others without government interference.
It is one thing to tell the government it cannot stop you from receiving a book. The First Amendment protects your right to do that. It is another thing for you to tell the government which books it must keep in the library. The First Amendment does not give you the right to demand that.
Second, if people can challenge which books libraries remove, they can challenge which books libraries buy. "[A] library just as surely denies a patron's right to 'receive information' by not purchasing a book in the first place as it does by pulling an existing book off the shelves." For good reason, no one in this litigation has ever defended that position.