...most fire departments I know of ARE Public workplaces. And as you just said, the government can’t tell us not to express ourselves.
Even so, public workplaces can define what is and is not part of a uniform, and what (if any) exceptions there are. The military is public but you can’t ‘express yourself’ any way you want on your uniform.
I think since the chief had allowed it in the past for this particular helmet, and the helmet hadn’t changed - but now all of a sudden the chief changes his mind, while it’s in his authority to do so, I don’t think he should have.