It is possible for a San Juan rabbit to have white kittens, as some San Juan rabbits carry genes for white fur. The color of a rabbit's offspring can also depend on the genetics of the other parent.

However, the San Juan rabbit is not a recognized breed of rabbit by the American Rabbit Breeders Association (ARBA), so the characteristics of a San Juan rabbit can vary widely. It's also possible that your rabbit may be a mixed breed or have genetic variations that could result in white fur. If the other parent also carries genes for white fur, then it is more likely that the offspring will have white fur. It's important to note that the color of a rabbit's fur can also be influenced by environmental factors such as diet, stress, and temperature.