What's the purpose of a "no politics" rule at work? Is to stop people starting shit with their coworkers, or is to give those in power an arbitrary hammer to apply to those without power in the organization?
If it's the former, 1) it should be just that and 2) it isn't needed because it's never ok to start shit with coworkers that is unrelated to work. If someone spends all their time starting shit, whether about politics (however that is defined), sports, food choices, clothing, or anything else you can just fire them. No need to have a "no politics" rule.
I think it's more simple. Just avoid any conflict. As you pointed out "don't start shit" already covers this but they specifically call out politics because some might not think it would cause offense.
What if you speak about something with no intention of creating conflict, but a few people around you get riled up? You haven't done anything wrong yet the divisive topic isn't a good fit for the workplace.
Some employees either can't or won't see this, hence rules such as "no politics".
If it's the former, 1) it should be just that and 2) it isn't needed because it's never ok to start shit with coworkers that is unrelated to work. If someone spends all their time starting shit, whether about politics (however that is defined), sports, food choices, clothing, or anything else you can just fire them. No need to have a "no politics" rule.