The answer is pretty clearly "no." But this position becomes more difficult to defend when the entire premise of the website is based on illegal content. Something like e.g. if YouTube was originally named ShareMusicIllegally.com.
Actually, at this point in writing my comment, I checked my facts. It turns out "revenge porn" wasn't illegal until Oct 2013, and then only in California. http://www.cbsnews.com/news/revenge-porn-banned-in-californi...
So this is a very unusual situation. We have a business built on a concept which wasn't illegal until recently. Did he continue to try to operate it in California after the bill was signed into law?
One position to take is "Who cares. This is a good thing."
That may be true, but remember that if you have the right to host whatever legal content you wish, then the first step toward losing that right is to not defend it. Sometimes that requires defending scoundrels.
Honestly, I don't know what to think. Maybe this isn't an instance of that sort of situation. On one hand, there are concerns about civil liberties in regards to webhosting. On the other hand, this website was clearly vile.
What does everyone think about how this has played out? Businessman builds a morally suspect business; business is outlawed; businessman is fined $250k. Did he deserve it? Perhaps it was karma. Is it a worrying trend that website operators are becoming increasingly culpable for user content? What if there were a subreddit dedicated to "revenge porn"? Should Reddit be liable for damages under California law, and should the subreddit be banned even though there are far worse subreddits, both from a moral and legal standpoint? So many questions (though most of it is conjecture, and hence may not be very useful).
EDIT: It turns out that the $250k fine wasn't due to user generated content, but rather because the website owner defamed someone by calling them a pedophile. So maybe the rights of website owners aren't even in question here. Was there any legal action taken against this "revenge porn" website owner stemming from the website after it was made illegal in Oct 2013?