I combine "chicken run" and "compost pile." The only things I leave out are ones that are downright poisonous (tomato leaves, potato leaves, rhubarb leaves--not much else.)
Yes, I even throw in things like green potatoes, and avocado peels and pits (chickens scratch them around, but they don't seem to actually eat them.)
Yes, I've put in moldy bread and limp vegetables and moldy vegetables and rotting apples and moldy cheese, and the milk left in a child's cup or in their cereal bowl. (Milk often poured over a sandwich crust or a burned pancake or something similar so it soaks in and is easier to eat.) Never had a problem.
The more choices you give the chickens (like a whole compost pile), the more they learn to pick what things will work for them.
I have never given large amounts of dairy, because the chickens have always gotten what was leftover from the people, and most of the dairy went to the people

(Yes, the chickens always had chicken food available.)
I've got a book on commercial chicken-raising from the early 1900s. It lists two chicken diets. One gets the protein from beef scrap, the other gets it from milk. For the milk, they serve it free-choice, as much as the chickens want. Obviously, their chickens were able to digest milk. I cannot believe the species has changed much since then. They are omnivores: designed to digest almost everything. (But I do agree that sudden diet changes can upset any animal, so small amounts are a good idea if the food is new to the chickens.)
Edit to add:
https://www.gov.mb.ca/agriculture/l...ltry/poultry-rations-and-feeding-methods.html
From 1945, Manitoba Department of Agriculture
"As a desirable protein supplement, milk undoubtedly heads the list."