How do i petition my school's new dress code?

What's wrong with not being allowed headwear? It's not really that big a deal, is it? You won't always agree with everything that happens around you, but I suggest you save your battles for something worth fighting over. Besides, it is considered very impolite to wear a hat indoors regardless what you see happening around you all the time. It's really not very respectful when you do. Hats should be removed any time you are inside, especially while sitting at a table eating. I wouldn't worry about it if I were you. Cheers!!