Not to take this too much further, but how does one define "unarguably"? Is it possible on subjective things like disruptive and offensive? I think not.
Any employer has a right to dictate what their employees wear at work, as a basis for working for that employer, as long as it doesn't discriminate one particular ethnic, religious, or gendered group. Hooters girls don’t get to wear pants, NFL players don’t get to wear tutus, soldiers don’t get to wear long hair, and I don’t get to wear my Batman costume to work. None of these are offensive in certain contexts, but are not the preferred dress code of the employer in question.
As suggested by Tero above, would you, under every circumstance, allow a representative of your enterprise to wear swastika symbol to work?