I don't always wash FQs and certainly wouldn't wash charms or jelly rolls. An exception to this is batiks which are notorious for running. I just spent all yesterday soaking some in first vinegar then salt waterand finally they went through the washer with a piece of white cotton that STAYED white!
Yardage I always wash and have recently started using spray starch which also has a silicon type thing in it (sorry the label's French and it says 'glisse' which means 'slide'). Apart from making the fabric crisp and fresh AND making the sewing room smell nice, I find this also seems to make the cutter and the needle slide more smoothly through the fabric. The kids like it too if some gets on the wood floor - they spend all day in their socks, sliding up and down! :D
An exception is when making One Block Wonders - then you don't prewash as you need the sizing to help align the layers. Those quilts I would test for colour fastness with a damp cloth and wash first time with a colour catcher to be safe. OR wash a spare piece of the fabric with the bit of white cotton to check for fastness. :D