Free speech/expression does not apply to employers/private workplace. The GOVERNMENT cannot take away your right to free speech. Private employers don’t have to tolerate speech or expressions of yours if they don’t want to. They have the freedom to set uniform standards and if you don’t like it, you don’t work there.
That said, the chief could have continued to make the exception instead of coming across as a ‘rules are rules’ kind of guy.
...most fire departments I know of ARE Public workplaces. And as you just said, the government can’t tell us not to express ourselves.