When a parent, a video store, a motion picture industry, or any private party, chooses to restrict speech, that is their prerogative. When a private Cyber Cafe or a parent uses filters, there is no First Amendment violation. Less clear are actions by library directors. Not all speech enjoys equal protection under the Constitution. That doesn't mean it's illegal.
Obscenity is legal in the absence of state or local laws to the contrary.
That is, obscene speech cannot wrap itself in full constitutional protection, but the government must have a rational basis for restricting the speech. The issue of defining obscenity remains. In a simplified hierarchy, they're not hard to understand. The gist of this goes back to state action. When the government makes a law, that law can be challenged as unconstitutional if a plaintiff claims it violates the First Amendment.