We never did remove the rings. The lady we got the chickens from said she tried to remove one and the chicken acted like it was very painful so she decided to just leave them in since they didn't seem to be bothering or stressing the chickens. We have done the same, though we have talked about removing them, we do not want to cause undue stress to the chicken or potentially cause a wound if there seems to be no reason to. The rings on our chickens are made of metal however, not plastic. If they were plastic I would think they would be easier and less painful to remove.
The lady we got the chickens from did remove the plastic spectacle parts (peepers) that shielded their eyes and said they were easy to remove. Most peepers/binders/chicken spectacles are ALL plastic and you just slip them on and off as you need to.