Hard rubber is not really rubber, it is a natural substance also called "gutta percha", a very common grip material in the pre-plastic days. While not a bad material, it has a tendency to become brittle as it ages and can crack spontaneously. It also can discolor, turning brown or greenish. Since original grips are a significant part of a gun's value, I would do as m.p. driver suggests and buy a set of plastic repro grips for shooting, while keeping the originals with the gun in case you ever want to sell it.
Jim