Pawnshops were allowed to remain open because they are used as "financial institutions" for many lower-income people. They were allowed to stay open for people to either pawn or sell items for quick cash. Remember, not everyone was lucky enough to keep getting a paycheck as we did.
Some cities classified pool supply stores as home improvement stores which is why they were allowed to remain open. Home improvement stores were allowed to remain open so people can make essential repairs to their homes if needed. Just because everyone stayed at home, didn't mean things in the home couldn't break.
Pet stores were allowed to remain open because pets need care too. They fell into the same category as veterinarians because the larger ones have onsite vets. Groomers are simply classified as "pet care" so they were allowed to remain open.
So, there are logical reasons why these places were allowed to remain open. It isn't absurd.