A private citizen cannot deprive anyone of their free speech rights. They have no force of law to prevent anyone from speaking their mind. They do have their own rights of private property with which they can limit what is said on their property. Which is entirely different than a governmental edict which can order the silencing of particular speech in an entire medium of communication. If Free Republic or DU choose to restrict what can be said by someone on their own site that person can go to one of millions of other websites or create their own.
As far as the issue of jury contamination goes the judge can sequester the jury or order that they may not view the internet or television or whatever. That is within the judge's purview. Silencing speech that he doesn't want the jury to hear is not. It certainly makes more sense to put restrictions on twelve jurors than on the six billion other people on the planet.
Sigh. That's the whole point, their jury poll has ALREADY been contaminated!