No, it should instead be influenced by the side that shouts the loudest in a Fox opinion piece.
The propaganda you decry is already well-embedded in our discourse. It's people shouting about Obama hosting death panels that will kill grandma, or how Biden will somehow turn this country into a socialist paradise, or how the Dems are stealing the election.
The kind of censorship you are asking for does not enhance discourse. It diminishes it. If people are creating policies that produce horror, they need to be able to stand in front of that horror, and affirm that they are okay with it. Not whitewash it with euphemisms, and statistics and 'this is uncomfortable to talk about.'