My son has a severe feeding disorder and almost never eats food served in WDW restaurants unless it’s fries. None-the-less, he’s always charged adult prices because that’s the rule and we know it going in. That’s why we choose where we eat even more carefully. Once, a server did give him the kid’s price, but we never asked for it. I’d say they can order from the kids menu, but they’ll be charged the adult price.
At the character breakfast in Epcot, you could tell the server felt really had charging us an adult price since the only thing he got was Froot Loops and didn't even eat those because there simply isn't much he eats. We in no way wanted her to feel bad, but she was going so far out of her way to try and find something for him, she clearly wanted to help. Bless her heart,