I'd definitely try to fix the door. First try to reattach the
"protrusions" using epoxy. If that does not work try to glue the shelf to
the door using epoxy.
Take the food to a friend's, turn off the fridge, and remove the door.
Let the door and the protrusions come to room temp. Epoxy and let cure per
the instructions that come with the epoxy. Reassemble and see if it's
fixed.Put in the shelf and add some weight. If not fixed then epoxy the
shelf to the door.