I second this question, and I actually *have* white handlebar tape. When I got it, the people at the bike shop said "Oh, just rub a little degreaser on any spots and it'll come right off."
Sure. Except the dye from my fuzzy gloves actually bleeds off the gloves and leaves red or black handprints on the white tape, and degreaser (Pedro's citrus stuff) is no good for that. Dirt also doesn't come off very well with degreaser. So I'd say degreaser = out.
My dad says just regular soap and water keeps his white bar tape nice and clean, so I may have to give that a try next. I'll let you know.