My understanding is that frozen foods that are not edible on shabbos are muktze. If so, if I have such foods in my freezer door, is it mutar to open the door on shabbos?

There is a general rule regarding muktze that indirect movement of a muktze item (טלטול מן הצד) is permitted if one is not moving if for the sake of the muktze item rather for the sake of a permitted item (S.A. O.C. 311:8). Therefore is one opens the freezer door for the sake of a permitted item, even though one indirectly moves the muktze item on the door, it is permitted.

However, there is another important point to discuss. An item which is holding a muktze item becomes itself muktze since it is a base for a muktze item (S.A. O.C. 310:7). This is called a bosis (lit. base) – בסיס. Therefore, since the freezer door is holding a muktze item, it itself should become muktze, and therefore the leniency mentioned above of indirect movement wouldn’t apply since one is directly moving the freezer door. However, there are several reasons why a freezer door doesn’t become a base to the muktze on it and therefore doesn’t become muktze.

1. 1. An item only becomes a base to a muktze item if the muktze was specifically placed on it, but if it was only placed there due to lack of space then it does not become a base (M.B. 309:19). Therefore, most of the time a person doesn’t want to place the item specifically on the door, rather he could place it anywhere in the freezer and he happened to put it on the door, and therefore the door doesn’t become a base.
   2. An item does not become a base to a muktze item if the muktze is relatively insignificant to the item it is on (M.B. 310:31). For example, a few pennies left in a drawer to not make the entire drawer a base since they are relatively insignificant. Similarly, a mukte item hanging on a door does not make the door a base since that door services the house and an item hanging from it would be considered insignificant (M.B. 277:7). Rabbi Shlomo Zalman Auerbach (שמירת שבת כהלכתה פ”כ סעי’ עט) and Rav Eliyashiv (שבות יצחק מוקצה פי”ב עמ’ קנג) extend this idea to the door of a fridge or freezer as well.
   3. An item which is a base to a muktze item and a non-muktze item does not become muktze (S.A. O.C. 310:8). Therefore, if there are any other edible food items on the door then the door would be considered a base for both items and would not be muktze.

In summary, one can safely assume that the freezer door is not a base to any muktze items in it, and therefore one can open the door on Shabbat, and the fact that the muktze item in it is also moved is muter since it is only being moved indirectly.