Yes. Yes. Yes. Yes.
Including the gray and white fabrics.
I recommend soaking each of the fabrics (only like colors together) in hot water for a couple of hours and then washing them - gentle cycle, cool to warm water. Dry until "barely done".
Imagine the worst case scenario for how that finished quilt might be washed. I would wash the fabrics, and batting (if it can be washed before it is quilted - not all battings can/should be washed.)before cutting them so there are no unpleasant surprises later.
Your fabrics may all be perfectly "fine" - and you might wonder why you bothered with the fussing.
Or you might find that you have a bleeder - and be grateful that you learned that before you made the quilt instead of after it was washed.
Others will probably give you different advice.