Notwithstanding any provision of law to the contrary, it shall be illegal to own, maintain, sell, or trade any canidae or felidae for which there is no USDA licensed rabies vaccine. Anyone currently owning or maintaining such animal may keep the animal for the length of the animal's life providing the animal is spayed or neutered and is registered with the Department of Agriculture and Industries. This section does not apply to any zoological parks, circuses, colleges, and universities, animal refuges approved by the Department of Agriculture and Industries, county or municipal humane shelters, the Department of Conservation and Natural Resources, or veterinary clinics.