“I don't believe there are any rules on how a British mayor should dress…”
No, I don’t imagine there are. Such matters usually depend on convention and the people involved exercising a little common sense and decorum. Two qualities obviously with which Mr Magid (who I’m led to believe has banned both Donald Trump and Her Majesty the Queen from his fiefdom) is not over-endowed.
As for baseball caps being worn back to front, I find it odd that the habit stems from a particular position in baseball. I should have thought that if the garment was clearly unsuitable for the task then something else might be employed. I shouldn’t imagine Mr Magid has seen service as a “catcher” in a baseball game (though you never know). I doubt much baseball goes on in Sheffield Town Hall anyway. Manufacturers go to the trouble of putting a badge on the front and the adjustment mechanism on the back. As well as that it must be plain that the peak is designed to keep the sun out of the wearer’s eyes, not off the back of his/her head so it shouldn’t be too hard to discover what way round it should be worn. Perhaps instead of a badge an “F” or the word “Front” should be embellished above the peak. Mind you, this would mean wearers having to have a matching clue tattooed on their forehead and they would also need a mirror to put the cap on. Perhaps not such a good idea.