If people can't keep their pets alive and healthy, the mental health impacts of isolation - as well as dangerous panic - will be much worse.
This is a small necessary measure to keep people calm.
Grooming activity can involve procedures which prevent illness or disability to the animal. It's not just a shampoo, it can be absolutely essential to the health of the animal.
I have no pets, myself, but really not going to get upset about PaH as "key workers".