[Preface ~What are accessories~]
Accessories are things that become yukkuris' symbols, like Reimu's Ribbon, Marisa's Hat, etc..
Yukkuris wear accessories from the time they are born, and as they grow, the accessories become larger and larger.
For yukkuris, the accessories are possessions more important than everything else, and have value equal to yukkuris' own lives.
If you'd ask why, that's because "Yukkuris depend on accessories to recognize each other".
Because of that, a yukkuri who lost her accessory wouldn't be recognized by other yukkuris, and will become the can't take it easy yukkuri to be bullied or punished by others.
And by wearing other yukkuris' accessories, this yukkuri is able to substitude the yukkuri who own the accessory.
(After sufficent training, yukkuris are able to recognize each other even when without accessories, though.)
The way how authors use the setting to illustrate their innovative yet charming stories is the spirit of yukkuri abuse.
--Anyway, if you're ever bored, just burn up Marisa's hat. There's nothing wrong about that.