My OH repeatedly cuts the contents of the waste paper bin and food bin into tiny pieces (for recycling purposes he says) Is this common? He was diagnosed about 6 years ago.
Its about as *normal* as any other of the strange things our loved ones do.
My late mother shredded tissues, picked bobbles off clothes and picked at buttons until the came off. ( And scabs until she bled!)
I guess if you have solid bin its pretty harmless and keeps him occupied.
( get pretty colour tissue paper,cottage industry confetti!)
Nothing is unusual with dementia. There is no harm in it, so I wouldn't think about how common it is and let him get on with it, always of course checking that he can't hurt himself.
My dad tears any cards he gets into a thousand pieces, he does the same with anything that comes in the post. Thankfully he always waits a day or two so I do get the chance to check his post.
Repetitive actions are very common in dementia. I think you are right that it is often a self-soothing action.
It drives you nuts, but if its not doing any harm then best to just accept it.