The purpose of a uniform is “uniformity” of employees.
There are lots of examples where Christians have been forced to remove a tiny cross pin, cross necklace or even a Christian chastity ring. (Google “employee told to remove cross”)
So I don’t buy your comparison.
That’s ridiculous, too - we should fight all of these infringements on frfee exercise of religion if they don’t impact the ability to perform the job. But it makes the argument for letting us wear cross pins at work much stronger if she gets a headscarf.