I need an ability to disable the auto downloading of hats when i start the game, because i want to delete the Contributors Hats because they look very Ugly, but im not able to!

Closing all issues as Hats has been rewritten from the ground up and the old mod for a long time now was no longer supported.. I'm sorry I wasn't able to address your issue. If you're still playing modded Minecraft, consider checking out Hats for 1.16.5+.

Hats now extracts the hats locally when it detects the extracted marker isn't there, so you can delete off hats you don't want after that now. I guess to a degree it's been addressed!