In point of fact, the American Library Association encourages every public library to have and implement an Internet access policy that both protects children and upholds First Amendment rights. Almost all libraries have such policies. Some require a guardian's signature to use the Internet. Some require parents to be present when children use the Internet. Some say you can lose your Internet privileges if you view materials that are inappropriate or offensive to others.
Some libraries provide filtering as an option for individuals and their families.
The important thing is these policies are developed to address their community's needs. They are not a government mandate imposed on all. The absolute best way to protect children when it comes to the Internet or just about anything else is for parents to supervise their children, to teach them basic safety rules and how to make positive choices. This means taking a few precautions, using common sense and practicing some good old fashioned family values - like taking responsibility for our own children and teaching them to live responsibly. As the tragic events in Littleton, Colorado show, that goes for older as well as younger children, something we librarians have been saying for a long time.