To be honest, I looked at the website, and most of the examples they have there were private companies choosing not to sell things (records, videos) they didn't want to.
Wether they thought they were obscene and weren't, or promoted ideas they were not comfortable promoting, private companies have the right to carry what they want, and private citizen have the right to exercies their right of free speech to speak against these ideas.
Free speech works both ways, but to hear the "artists" talk about it, they should be the only ones allowed to express themselves, and everyone should be forced to listen to them.
Check the definition of censorship, and you'll see that most of these examples do not fit. Most of these people were allowed to write or produce anything they wanted, but there was no guarentee they were going to be played or promoted by anyone other than themselves.
There were a few cases where performers were asked to change the lyrics, adn a couple where they were changed without notice, and I would agree that would be censorship.
I think people (the market) should decide what they can and can not hear, but companies also have the right not to play or promote anything they don't want to.