I have always composted animal by-products whether that is left overs from human or cat food, or dead critters that one finds around and about.Here animal by products are not allowed in public composts. I think the main reason is to avoid rats, and other bigger animals that could try to get in there.
We don't generally put animal by products in composts even on private properties. I'm surprised to learn it's different elsewhere !
Bones take for forever to break down so my compost always has bones in it.