These comments are for items that will probably require washing at some time (I haven't done wall-hangings, but I just took a couple of cloth items down yesterday - they are very dusty and I think they need to be bathed)
Two reasons why I wash/shrink all washable components of an item before cutting them:
1) I'm frugal (I hate the word 'cheap') - I see no reason to have to spend additional money on Retayne, Sythrapol, color catchers/grabbers, or any other color fixatives or color removers. If there is a serious issue with a fabric, I want to know about it before it's part of a project. If I wanted to play with those chemicals, I would learn how to dye fabric myself.
2) I'm lazy (I will have to think of a better word for 'lazy') -
a) I don't want to spend any time on trying to remove color/dye from surrounding fabrics
b) I don't want to try to block something back into shape because of uneven shrinkage or the fabric reverted to it's natural state
c) I want the item to not require 'special handling' when it's laundered
c) I don't want to have to 'think/worry' about how a particular item will look after it has been washed (assuming the item has not been bleached, burned, or torn)
I have had a couple of 'not so great' experiences - so that's why I'm so seriously into 'preventive maintenance' - it's just easier for me to spend an additional few minutes prepping than to spend hours trying to undo a mess that could have been avoided.
I know there are many on this board that say they have never had a problem, or don't see any shrinkage - I have -