I decided to play recently (yesterday) to notice my spider wasn't wearing a hat and after checking the customization menu it said I had no hats.
This persisted even after uninstalling/reinstalling and checking file integrity on Steam.
Lastly I was able to reacquire the hats through the same means of acquiring them. Namely, I got the cone hat from jumping off the map in the lobby. Regardless, I'd rather not have to do that for all the hats I'm missing.

