I've seen a few jokes popping up here and there online about how public libraries (and libraries in general) are a place people go to surf the internet for porn. And speaking as a librarian who's worked in both places, it's true: a number of people come to the library for that purpose. We don't filter our internet access (though some public libraries do, depending on the local regulations.)
And I've had a number of people ask me why the library doesn't filter. Why is it that the American Library Association is dead set against it? That link gives some excellent reasons, but I wanted to give some of my own insight.
The main goal of a library is to provide access to information. As soon as someone--a librarian, a politician, a parent--starts trying to limit that access, bad things happen. What sort of bad things? Well, what one person might consider obscene, another might consider art. Obscenity is a hard thing to define, and it changes from one person to the next. (Again--this is experience speaking here.) Even if we could all agree on what was obscene and inappropriate for a library, actually filtering just that content is extremely difficult. Technology inevitably filters out some things that shouldn't have been, and misses some things that should have been, if that makes sense.
So then staff are constantly fielding questions from patrons about why _________ site was filtered or why ________ site wasn't. In many ways, filters give people a false sense of security. They feel like the computers are "safe," where in reality, they're just "safer." In the end, it's better to leave the decision up to the patron. Let them decide what is appropriate and what isn't. Yes, I realize it's taking things to extremes, but all you have to do is to look to more totalitarian regimes like Iran or China to see what government-mandated internet filtering can lead to--and then realize that wherever you draw the line on what "should" be filtered, there are going to be people who disagree with you.
And at the heart of the matter is the single driving fact that libraries exist to inform people. Filters exist to keep information away from people. The two don't usually get along very well. Better to have an informed group of users who know what they're searching and why.