It's different for every person. It's not really logical. I used to eat bananas and parmesan cheese (sprinkled on lettuce) and those foods are often on a lot of people's unsafe list. Then again, I could never eat yogurt or almonds (when I found out they were seven calories each and two calories from fat, I felt more betrayed than Jon Snow) but a lot of anorexics would totally eat these.
Generally an anorexic will find a few foods that they feel they can eat and portion safely, and have weird obsessions with them. I would down packets of aspartame and binge on frozen corn (your body can't process the nutrients in that form). A lot of anorexics will eat rice cakes, though I never could because carbs. Diet Coke is an entire food group. Seriously, even though it hurts like a ***** to swallow, you just constantly down it. Obviously green tea, lettuce, celery is a big one.