I am a fan of prewashing for many reasos and that includes scraps. Basically, if it is a fat quarter or larger, I treat it as fabric yardage and just wash with like colors and my normal wash. I do watch to get them out of the dryer just before dry and press hot to a crisp finish.
I do cut off any long stringy ends or ragged bits both before washing and then as I take things out and before I put them in the dryer, I cut off any tangles and give the fabric a nice Snap! (you'll know it when you hear it) and toss it in the dryer.
Small bits I wash in lingerie bags or inside pillow cases that I tie shut (I use hair elastic actually).
The worst things to wash in my opinion are long skinny pieces. It is hard to make me wash/use precut jelly roll strips for example. If I felt I couldn't use them without a prewash, it would probably be more of a gentle sink/hand treatment. And I'd probably just not bother and cut something similar from my already pre-washed stash.