Does the contemporary U.S. government pursue people with unpopular opinions, as in Fahrenheit 451?

Now that is an interesting and difficult question! I think my answer would be, "sometimes". While The American people are 'free', we are not completely free. It is not a perfect world and we must protect ourselves as a nation. The question is, "How much should we protect ourselves as a nation, and who is a threat?"

Look at the oath of citizenship...

...I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic.

...enemies, foreign and domestic. The Government of America believes that some Americans are its enemy and that it has the right to spy and to check that nobody is a threat. This spying and snooping (or pursuing) has got much worse under the Bush administration with The Patriot Act.

http://en.wikipedia.org/wiki/Patriot_act

Until recently the most pursued opinion was Communism. Even though The Constitution gives you the right to be a communist, and that there is nothing illegal about communism. The Government has always tried to crush communists. And has locked them up and even executed them. America doesn't like to talk about it, but in the 1950s the American Government went out of control and started attacking its own people. Back then, if you criticised the government at all, they called you a communist (even if you weren't) and made your life very difficult.

http://en.wikipedia.org/wiki/McCarthyism

But, on the other hand, some American citizens are very dangerous. Gun nuts and far right extremists for example. In 1995, Timothy McViegh blew up a government office and killed 168 people because he believed the American Government was a crypto-socialist plot (he was a loon basically)

http://en.wikipedia.org/wiki/Timothy_McVeigh

And foreign organisation operate secretly inside America and the American government should try to find them (Al Qeada for example) Then there's The Mafia and Drug Cartels etc etc.

It is very hard to say how much 'pursuing' the government should do. Would you like it if they read your emails? (Because they do). Would you like it if they listened to your phonecalls (Because they do). Would you like it if they checked what books you get from the library (Because they do). They can enter your house and leave again without telling you. And, under George Bush, the American Government locked people up for years and tortured them without telling anyone why!!! (in Guantanamo Bay)

The government is sometimes more trusting and sometimes less trusting of its citizens, under Bush, a republican, The American government became very suspicious of its citizens.