I've had rabbits and ground hogs test out new peony noses to see how edible they are. Fortunately they've realized that these shoots are just not the best things in the garden to eat and don't usually do it again. Of course any of their relatives might also come over to test the potential 'salads' you are growing so the problem may continue

Unfortunately even the birds can trash a clump of fragile new noses (males fighting at mating time) so our peonies are never really safe. How much do you want a garden covered in wire netting?

I have too many and scattered peonies so not practical - the peonies are not killed and will live to bloom another year. Grow lots so there will always be peonies to avoid the foraging and bloom