Christmas cactuses can cross pollinate, but the effect will only show up in offspring that develop from seed. In your case, the color shift that you noted in the white Christmas cactus is most likely due to slightly different environmental conditions. At cooler temperatures a pigment called anthocyanin, that causes some red colors in flowers, is more likely to have an effect. You may often notice this in white chrysanthemums and other white flowers. They may be pure white at warm temperatures, but take on a pinkish cast when it turns cool.