I have one white hen, and she is fine unless she goes free-ranging. Then she rolls in the dirt so much that she looks nasty for several days. Or if it rains, she is all muddy looking. (Hopefully that will not be a problem now with their new rain-proof pen roof!) The others get just as dirty, but don't show it as much.
I used to have a white horse, and will not ever get another that color, because of all the work to keep them clean looking, and I find the same issue with white chickens. I like all my animals to look clean and neat, since family tends to drop by at random with their kids, and I want the kids to stay fairly clean petting everything, and also for them to look appealing to my guests. Since I live with my in-laws, who aren't really farming types, I try to keep everything as spotless as I can to impress them, too. (I don't want them suddenly deciding they don't like smelly dirty animals everywhere!)
I also just don't like the color that much on chickens...I find other colors more attractive. Ironically, I have an incubator full of white plymouth rocks right now...