Greys are lactose intolerant hence they should not have dairy products but I think the process of making yogurt removes the lactose so they can eat it, a little bit of cheddar cheese is also good for them but in moderation.
You are right about the no mushrooms, no chocolate, no caffeine, no avocado and no carbonated drinks, you will find a list of forbidden foods in the bird food room along with vegetables and fruits they can have.