Shoes and their rack should travel apart. The shoes are heavy in bulk and the rack itself is often thin wire or light shelving that bends if it takes on that weight during a move.
Pro tip: Use a shoebox or a bag with a clear window to keep pairs sorted and easy to spot when unpacking, rather than one giant mixed box.
Watch out: Never carry a loaded shoe rack; even a modest collection of shoes adds enough weight to bend thin wire shelving during the tilt of a carry.