Opals are partially composed of water. It is a good idea to store them in distilled water.
I think chrysoprase is what happens to a certain type of opal when it dries out over a long period of time. It loses a certain amount of water and its opalescence disappears and it becomes apple-green. As it loses more water, its color pales to light green, then yellow.
I have never heard the recommendation that chrysoprase be stored in water, though. At rock fairs, I always see the opals stored in water when they are not set in jewelry.
Turquoise, lapis, and sodalite come to mind as stones that should not be placed in water. However, if a stone is tumble-polished, the tumbling process creates a barrier that keeps the actual mineral from contact with the water. Thus malachite, which has copper in it and is unsafe for elixir use in its raw form, may safely be used in its tumbled form.
Barrier or not, it still makes me a little nervous. I wouldn't subject them to anything more than a quick rinse. There are other ways of cleansing stones. That's usually the concern when the subject of water comes up.