The US has always had a strong puritanical streak. Part of it is that when Europeans migrated to America, many of the people who decided to make the trip were various religious sects which were just a bit too extreme and too weird to be accepted at home. And they brought along some strong ideas about what you weren't allowed to do. The prohibition laws were spearheaded by such religious groups, for example.

This all got a boost in the 50's with McCarthyism and the Cold War. America felt it was in a competition to prove its way of life superior, and so it had to become as anti-communist as possible. Whatever they did, we had to do the opposite*. Communists were opposed to religion, so America embraced religion, and became far more religious than it was a few decades earlier. And this, naturally, gave more power to the religious groups who were still around, and who still didn't approve of nudity or books with bad words in them.

Of course there's more to it than that, but America has always been quite prudish and puritanical.