I don't see a problem with it. If someone is paying your wages they pretty much get to make the rules. As long as it's a blanket policy and not one person getting singled out, run with it.
They also banned jeans and t-shirts with logos? That's a no brainer, depending on the job. I'm not supposed to wear jeans to work, but will when I'm not going into the office. As far as t-shirts with logos??? Who wears those to work, at least in a professional, municipal, deal with the public kind of setting?