Though user @JordanS has delivered an excellent, well-informed synoptic answer, more can be said.
First, the question is appallingly American, by which I mean historically provincial. The state can prohibit pornography or anything else because it is "the state." The "state" is not to be confused as an entity with the government, the people, the nation, the economy, the history... or all the other systems that fall vaguely under the false identity "america."
The "state" is not necessarily responsive internally to its citizens. It is responsive externally to other "states." To perserve itself it must continually adjust its internal relations. This includes, above all, the distribution of information. For example, the "financial" information on your computer enjoys different, and usually stricter, legal protections than the "sexual" information on your computer.
This is quite reasonable. As a "financial" or "sexual" being you are never an isolated individual. You exist only in relation to others. The state, for better or worse, will configure these relations, and they will evolve. Unless you are a confirmed solipsist, you have no absolute "right" to privacy... or to anything else. Your "rights" will evolve in relation to your dependence upon the state, which is typically absolute.
However, I must add that a small minority of your fellow citizens do not depend on the state. The extremely wealthy live under an international regime and can select the legal or moral "rights" they enjoy in ways that wage-earners inside states cannot. This seems like a long way from your question about "pornography." But it is not. It concerns "rights" within "states." What is pornographic is the financial violation, or "rape," of the implicit social consensus manifested in the state.