As a retired groomer, one thing people don't realize that when you pick up your animal at the groomers and laugh about it, it does make the animal feel bad, because it had been shaved.
I also tried to talk people out of doing it.
I have seen dogs sitting so proud and the owner laughed at them when picking them up, and the dog drops it's head and cowers, they would often hide when getting home.
I always told my clients, no matter what, do not laugh at them, praise them. They feel good when praised, and to please tell those at home to do the same.
This poor kitty could have had something like that happen, and it is embarrassed to go out now. It could also feel unsafe to be outside.