Students don't, although they do send you 3 ATP polos when you sign up for the ACCP. Instructors have to wear an ATP shirt and closed-toed shoes. I don't think there's a policy against shorts, which is a great thing since those Seminoles can get a bit warm in the summer
I never read or heard anything that they are required. They are nice on checkrides because they have a collar (that IS required) and looks good for the company on the XCs. My shirts had a hard life, with many oil and grease stains,so I would not want to wear one on a checkride!