You could wash the backing if you want, but I would advise against washing the cut pieces for the top. I did one of these kits and much of the fabric was red. I simply did its first wash in a machine that uses a *lot* of water (to dilute any bleeds) and Synthrapol (which suspends loose dye particles in water so they can be rinsed away instead of settling into other fabrics). It came out fine.
In terms of shrinkage, it doesn't matter if the backing fabric is prewashed and the pieced top is not. Once the layers are quilted the batting takes control of shrinkage, meaning that with moderate quilting the batting prevents fabrics from shrinking more than the batting shrinks. (If quilting lines are 10" apart, then this does not hold as the shrinkage across 10" of fabric could exceed that of the batting.) In other words, fabric shrinks differently when washed by itself and when washed after it has been quilted to a batting.