Jeans are perfectly OK in the Celebrity MDR. Shorts are allowed during the day but are not allowed in the evening. I've seen this enforced with adults. I don't know if they would cut some slack for a teen.
For you question, I think it is easier to look at what is prohibited. In the case of Celebrity, it is the following:
"T-shirts, swimsuits, robes, bare feet, tank tops, baseball caps and pool wear are not allowed in the main restaurant or specialty restaurant at any time. Shorts and flip-flops are not allowed in the evening hours."
BTW, the way I read this, hats or caps other than baseball caps apparently would be OK. That means my Dad hats would be allowed! 😄