It doesn't help that "freedom of speech" is broadly taken to mean that the government can't restrict your speech. However, most forums where people congregate to speak are not managed by the government, but by corporations.
And most people seem to find it totally OK for a corporation to silence any speech they want to.
Most people find it OK until it is their own speech being silenced, and then they have a problem. It's one thing when NAMBLA is banned from a social networking site, and another when your anti-war group is banned.
That aside, there is an important difference between corporations and the government: corporations do not typically have the power to imprison or kill people, and when corporations want to impose a penalty they must ask the government to do it on their behalf. GoDaddy can refuse to provide service to nazis, but cannot do anything about nazis choosing some other registrar. A government can imprison people for running a nazi forum, even if the nazis set up their own registrar and maintain their own hosting.
And most people seem to find it totally OK for a corporation to silence any speech they want to.