Not sure anything will 100% prevent color changing. Take something like purple heart - it oxidizes and the purple gets deeper over time, I don't think it fades. Oils in the wood may still migrate a little. Stabilizing will slow it down tremendously, but not sure if it will prevent fading in all cases.
I did a set of Cocobolo handles (not stabilized) and had a good, complete finish of tru oil on all surfaces. They are much much darker 2 years later. Stuff changes, even when finished and stabilized. But finishing (and stabilizing) should minimize it.