Freedom of speech means the government can't throw you in jail for saying something they don't like. It doesn't mean other people can't tell everyone what you said and ostracize you for it. So, it's definitely not a freedom of speech issue.
That being said, our society is going to have to adapt to the internet and the concept that someone can say something they regret later. These stupid racists can be held accountable for what they're saying, but if they mature and realize how _stupid_ they were, I don't think they should have to deal with someone combing their history and holding it against them. (EDIT2: I mean, ten years down the road, if they're no longer racists, they shouldn't have an employer refuse to hire them over it.)
But these are the sort of people that use social ostracism and even threats to oppress other people, and they deserve to have the full force of that tactic turned back on them until they stop doing it. They punched first, and they need to be punched in return until they stop attacking others.
EDIT:
Basically, I think people have, and should have, the _legal_ right to absolutely ruin these assholes' lives over this, to shun them and refuse to hire them and pretty much treat them like they want to treat everybody else. That being said, morally, a little restraint and mercy is always nice, and helps preserve civility.