Moderating it and encouraging the community to run around policing each other seems like it is a bit too much.

No matter how gently you moderate a person many take it harshly and I suspect the response will be to push back at the moderator, moderation, and ultimately the rule.... and it ends up being more counterproductive than anything else.

Very very generally I would compare the response to say police detaining someone as far as a someone's response goes. It is hard to do so no matter how lightly it is presented and not get a strong response.

Another issue is that moderators can't know if two people know the correct pronoun unless clearly stated in that conversation, so they are going to be guessing the vast majority of the time...