The argument that a GPS used by a passenger might be a prelude to terrorism is disingenuous. On nice days (no cloud cover,) anyone with a reasonable map/atlas (and a fair comprehension of geography) can tell exactly where the airplane is by looking out the window. Should we ban windows? Ban books with maps? Why not just be completely safe and handcuff all passengers and place light-proof hoods over their heads?
Additionally, as airborne web access becomes more and more available, the information on the whereabouts of ANY flight over the United States is freely available from the FAA, including altitude, airspeed, direction, etc. So, if we ban GPS for paranoid terroristic thoughts, then we will have to ban/halt the soon-to-be widely available internet access, too. (BTW, that won't happen.)
Many common GPS units won't even work on a jet aircraft. They are programmed to stop functioning when a certain speed is reached. This is an intentional part of the programming by the manufacturer to preclude pilots from using a handheld GPS intended for ground/water use in their airplanes. It's intended to fend off lawsuits and liability. They figure that if the unit is moving at, say, over 150 mph, it's NOT in a car or boat and is not being used as intended.
That being said, I believe that the (rather expensive)units that are specifically designed for use in aircraft are all TSO'd (i.e. they meet the FAA's Technical Standards Orders.) This means that they have been tested to NOT interfere with aircraft systems and navigation, since they ARE an aircraft system in and of themselves.
Each airline does indeed have the right, unless prescribed by law, to dictate just what can and cannot be used on their aircraft. They can make this judgement as arbitrarily and whimsically as they care to. The banning of TSO'd GPS units in the cabin is just that. An arbitrary decision made because it's much easier to just say no than to think things through. (Few airline managers are able to think things through, BTW.) If there becomes a demand to use these "legal" GPS units, the airlines who allow their use will attract those customers, and the market will make the adjustments based on competition.
I travelled on Malaysia Ailines a few years back and found that portable CD players were banned! The F/A stopped me from using it and pointed it out in their in-flight magazine. Needless to say, I scratched that airline off my list. What utter nonsense! It makes every bit as much sense as banning the "legal" GPS units.