Not that i agree, but i can see why the school is enforcing this - some kids would take it to the extreme and end up with lil holes all over their faces, just to rebel IYKWIM??
I had a nose ring at that age and i probably still would if it werent for my boss at the time - i told him he couldnt discriminate against me!! And he replied that as i was casual, all he had to give me was 3 hours a week.

I succombed to the corporate BS, lame little activist!

Help your daughter to fight!! But ensure this petition is clearly within reason - dont leave it open to interpretation (eg multiple piercings) - there should be no reason for them to deny her wearing a retainer for crying out loud.
Go to the P&C meetings. Arrange a 1 on 1 with the principal. If your daughter succombs to thsi it may just well shape her view on "authority" forever..... hang on, that is probably a good thing!