It is easier to answer that question by explaining what does not freeze-dry well. Products high in fat or sugar don't freeze-dry well. Examples are maple syrup, honey, jam, pure chocolate, nut butters, butter, mayonnaise, and other straight oils. Often, foods containing one or more of these products in limited quantities can be successfully freeze-dried. Generally, the higher the fat content of a food the shorter the shelf life.
Some of the specific products people wonder about:
Alcohol does not freeze-dry at all.
Butter and oil will not freeze-dry. In small quantities in products it does well.
Shredded cheese freeze-dries great.
Milk, nut milks, kefir, and yogurt all freeze dry very well.
Bread, cookies, cakes, and muffins can be freeze-dried but the process of rehydration tends to leave them soggy and undesirable.