Sorry, dad's shirts are not forbidden. Lol. Here are Disney's rules for theme park attire:
"We suggest you dress comfortably, wear good walking shoes and check the local weather report before you leave for the parks at Walt Disney World Resort.
Proper attire, including shoes and shirts, must be worn at all times. The parks are a casual, family-oriented environment. Ensuring that the parks are family friendly is an important part of the Disney experience. In that spirit, we ask you to use your discretion and common sense.
Attire that is not appropriate for the parksand which may result in refusal of admittanceincludes but is not limited to:
Adult costumes or clothing that can be viewed as representative of an actual Disney character
Masks
Clothing with objectionable material, including obscene language or graphics
Excessively torn clothing
Clothing which, by nature, exposes excessive portions of the skin that may be viewed as inappropriate for a family environment
Objectionable tattoos
Adults can visit the parks if their hair (or makeup, if applicable) resembles a Disney Princess or character, provided that they are not also wearing a costume or clothed to look like the character."
So, in most restaurants he will be ok. In signature restaurants, it's business casual, I believe, and in Victoria and Alberts, I know you need a dinner jacket and perhaps a tie. Not sure about the tie.