Brady's personal chef Allen Campbell has reported that the quarterback avoids "nightshade" vegetables, a category that includes tomatoes, peppers, and eggplant. Brady seems to steer clear of these items either because he thinks they cause inflammation, or because they supposedly aren't anti-inflammatory.
Brady also reportedly includes mushrooms on his don't-eat list, but those aren't nightshades — they are fungi and not from the Solanaceae plant family.
The vegetables Brady won't eat are in reality extremely healthy and do have anti-inflammatory properties. A food allergy or other sensitivity is, of course, a reason to avoid a certain vegetable. But most people should not cut these foods out of their diets.