Both the Klan and Nazis are political organizations so supporting them seems pretty clearly political speech. Similar, you wouldn't be allowed to wear your Klan hood or your Bernie Sanders hat to a polling station (where political displays like that are prohibited). (Although, of course, people probably wouldn't notice the Sanders hat)
You're going to throw accusations like "supporting the klan" or "supporting the Nazi party" around with only circumstantial evidence? You're one of those political discussion agitators after all.
These two fellows just think that the hats and armbands they're wearing are stylish accessories. And the hand motions? No more than a good triceps workout.
Suppose we worked at a sporting goods store and management noticed that employees and customers were regularly getting into arguments about teams, players, game outcomes, etc. So, management says to employees "Employees should not discuss their own personal views on sports. This will help us better serve customers and work together."
Well, once that new policy is in place, it won't exactly be a head scratcher as to how we should view an employee wearing the jersey of his favorite basketball player. Personal opinions on sports are out and wearing a sports jersey is clearing showing, or at clearly will be interpreted as showing, support for that basketball player.
My argument is that your preferred work policy - "appropriate discussion" is impossible without a lot of implied use of your least favorite policy - being "told what the answer is."
In turn, your second policy - "no political discussion" is practically unworkable. I demonstrate by an example. If you want to make it so your coworker can't wear his swastika, you must allow political discussion:
"This piece of clothing has a certain understood meaning in society, wearing it implies he supports xyz, any claims to the contrary are a fig leaf."
"No, no, I just like the look..."
And we have a political argument on our hands about whether such attire is appropriate.
In short, allowing no political discussion at the workplace is not possible.
As to your own metaphor, it falls flat. Everything is politics. Not everything is sports. It is very possible to go about your day without making any sporting statements, and impossible to not make political statements.
I think there will be ambiguity and good faith discussions and clarifications to settle expectations. I also think that people who insist on it will always be able to split hairs and invent arguments.
If the company has a policy that says "No unwanted touching of coworkers" and one employee hovers his hand over coworkers while taunting "I'm not touching you" the problem is not with the guideline. Likewise, if you say "No politics at work" and someone keeps coming up with creative arguments of the form "Technically isn't this politics" then the problem isn't with the guideline either.
