I like this idea as a starting point. It’s easy and doesn’t limit your options - if it doesn’t work you can move to a different solution.
(Personally I’m a big fan of earthquake putty. With three active cats in the house, I’ve had plenty of occasion to use it as a quick fix/preventive measure. It rarely fails me.)
if the issue is the shelves move, then also try lining the ends of the shelves with duct take (cut to size) to make the shelf a snug fit. (or a thickness of cardboard, or for real fancy, that iron-on veneer. The less the shelf moves, the harder for the pins to work loose. But again, use duct tape or something to press fit the pins so they are not loose.
Another solution is - why use just pins? Get longer pins and a thin piece of wood, say 1/4"x3/4" x depth of shelf. push the pins as far in as possible and glue to wood strip to the pair. Now each end of the shelf rests on a ledge 3/4" wide, and it’s harder for 2 pins to simultaneously work loose than for 1. (Same idea as the quarter-round, I imagine?)
You can glue or double stick tape 4 small blocks of wood to the bottom of the shelf, 1 behind each pin location. The goal being to prevent the pins from backing out, the wood block stops it from moving.