I've been rolling this around in my head as the discourse has gone on. I don't know if anyone is talking about the same thing. I think 'normal' just sucks as a term tbh. It has inherent reactionary undertones, and can mean anything from "sit down and shut up, take the L, moderate your positions" to "don't be antisocial, don't jump to hostilities, assume good faith." Fuck the former, but I think the latter is important.
Anyone trying to express the latter would be well-served by reframing it as "be cordial." You cannot have a movement if you can't be cordial. You will not be able to organize with people you are ready to deem an enemy without further investigation.