There are many misconceptions about this being reported. The zoo did not ask for just any unwanted pet (they also themselves didn't even use the word for pets). They specifically mentioned chickens, guinea pics and rabbits, as well as horses. They also never stated they wanted "unwanted" animals, but rather animals that were already going to be put down for various reasons. The zoo will then euthanize the animals, and make sure they are not sick before feeding them to the zoo animals.
Dogs and cats have also been mentioned a lot, by people debating the topic, but those are not animals that the zoo accept. From
an article talking about the post getting so much attention from abroad, the zoo says: "We don't accept dogs and cats. Predators don't really eat predators, but instead prey animals, which is why those are the ones we focus on getting". Another
news site also reported exactly which animals they have recieved so far this year which just included horses, rabbits, chickens, guinea pigs as well as trouts.
Another misconception is that this is something new the zoo is doing. In many Danish zoos it's common to ask people to donate animals that are already going to be put down, to use as feed for the animals. The zoos prefer feeding whole animals (or larger bits), as there are many benefits and it reflects more natural behavior in the animals. Zoos will also feed their carnivores giraffes and zebras that have been euthanized.
I think most of the outrage about this is based on misunderstandings of what the zoo is actually asking, and I would be surprised if this entire thing is unique to Danish zoos. The carnivores need to eat, why not let them have animals that were already going to be put down?