No, because, by shaming someone to stop posting, you would be silencing speech that you don't like. That would be censorship. And we don't want that, do we?

Last I checked,in the US, the 1st amendment protects people's right to protest something they don't like. Sure, no one has the right to "Not be offended", but people also don't have the right to "Not be criticized." It goes both ways.