Hanging food in a shelter does not attract mice. Eating at a shelter does attract mice; and I don't mean eating in a shelter, just eating at the picnic table is what attracts the mice.
Also, the shelter itself attracts them, because it's shelter; in the same way coral reef (or man-made reef) attracts many organisms as opposed to barren sandy bottom, because it provides shelter.
If you notice food hung in shelters isn't stolen by mice, provided one uses a mouse guard and doesn't place a bag against a beam. However, leave some food in your pack and I guarantee it'll be gone in the morning.