Start with the entirely unnessecary carniverous apex predators (aka pets) people insist on keeping. If people cant get rid of pets, then asking them to avoid replicating their own DNA is going to be a challenge.
That said I have said no to dogs myself - mostly because of cost and the constant need to be looled after - and the animal we do have is a rodent that we got second hand, meaning that food cost is leftover carrot shavings etc + a bit of hay