I haven't but have been contemplating it. I did cut the tags off the bedding pieces and am planning to cut them off the toys that hang over the bouncy seat, etc....just haven't gotten to that yet.
I have been thinking about cutting the tags off mine too... I suck at washing clothes and I am always reading the tags about how to wash things and I thought maybe I should... but you are right it is really big and annoying lol.
Re: Boppy pillow cover
Yes.
I think you ask a lot of silly questions, fwiw...