Pantry shelving is only awkward because it is usually still full of food when moving day sneaks up. Clear it completely, break it down into its flat sections, and it packs like any other flat-pack furniture.
Pro tip: Sort pantry food into a cooler bag and a dry box before disassembling shelving so you are not juggling groceries while you have a wrench in hand.
Watch out: Do not force a stuck bracket loose with a screwdriver as a lever; look for a release clip first, since prying can bend the wire or crack particleboard.