I like both of the above. I was picturing a light blue as a read it. I do love the apple green idea too, especially if you had a lot of white in there like shelving or something, but it might be tough to pull off right next to a sage green. Dunno.
For some reason I really love colorful laundry rooms. Mine is navy with white beadboard. I like FormerlyRR suggestion of aqua or turquoise or maybe a dark purple?
The possibilities are endless! Use the red w/d as an accent and pick a color from there. I prefer cool colors, so I would go with blues, blue green or a silvery grey. To do more fun, consider doing stripes, either tone on tone or on the white, you can also do different finishes for contrast. Few ideas: Dark blue, silver and the red White and silvery grey stripes and red Royal blue, gold accents and red (see previous post about powder rooms and dark colors).