"Fastidious creatures" refers to animals or beings that are very particular or fussy about their surroundings, appearance, or cleanliness. They are known to be very careful, precise, and demanding in what they prefer or accept. Full definition
Cats are naturally fastidious creatures and are very clean in their habits, and it is not normally necessary to bathe your cat as they do this daily themselves. (second-opinion-doc.com)
But there is one very unique behavior that is inherent in felines: they tend to cover their droppings and drippings in sand to help mask the smell, and perhaps because these are very fastidious creatures we are talking about. (mypetneedsthat.com)