This isn't separation of Church and State as there isn't necessarily any inherent relationship. Wearing these items has nothing to do with anything because a non-religious person could just as easily wear this stuff.
It's kind of silly and not practical, and they may as well go so far as to enforce a uniform and be done with it. If people can be influenced by the wearing of a hat then they can be just as easily influenced by the choice to wear anything else, and if they're more concerned about wearing their own clothes than working for the state, then maybe their judgment can't be trusted.
Separation of Fashion and State. Am I right?