I think you're kinda screwed either way, actually. Words do hurt; you can tell people to just tough it out but it means that you end up conceding large amounts of the political space to the ones most willing to be cruel and least injured by being defamed.
I'm not calling for speech policing here. I'm just pointing out that the real people who participate in political processes are subject to human failings. It's not a logical conversation; it's emotionally charged rhetoric. So just saying "everybody says whatever they want" amounts to a different kind of censorship. It may well be the most unbiased form of censorship and the one that is most "just", but it's not without downsides.
You see it in social media all the time. Trolls can shut down conversations. Web sites that don't want to be primarily about trolls and up providing tools to reduce their visibility, one way or another. It's often called "censorship", and in some senses it is, albeit not government censorship because it's not a state matter. The national conversation is a state matter, and a state may well want to think about what kinds of tools are appropriate for keeping the conversation civil and productive.
Again, not calling for censorship. I haven't got any policy to offer. It's just that I think it's important to recognize that free speech has non-obvious feedback loops that make it less free than it appears.