Only once have I ever made an important criterion out of color - or rather on NOT being a color. When Sabra, the Ultimate Cat, my first Siamese, died, and I picked out a cattery for Meezer #2 (who turned out to be HRH Rosalind) a few months later, I simply could not deal yet with having a cat look very much like Sabra and not be her. So on “color preference” on the kitten waiting list form, I wrote, “Anything EXCEPT chocolate.” That plus my wanting a female jumped me up the waiting list when HRH made her solitary entrance into the world. She was a singleton, of course. From the beginning, she has not been interested in sharing. People were in line for seal females, lilac females, chocolate females, and blue males, but nobody had spoken for a blue female, so she was offered to me. She was refreshingly her own cat and nothing like Sabra. That restriction has faded a bit over the years, and I am sure that someday, I will have another chocolate.
I did pick up Emily Dickinson, head barn cat, based on color, but that was for her sake, not mine. She is black, was in the city on the streets, and Halloween was approaching. I feared for her. (Mom had a black cat in her childhood who had her throat cut on Halloween.) So I trapped Emily and exported her to the farm.
But in general, color does not matter to me.
ETA: Just realized this is my reply for cats. For dogs, I do prefer very dark, if not black, for security reasons. Woman living on a rural farm, and I’ve often heard that black or very dark dogs are more off-putting to potential criminals than the same-sized dog in a different color.
