There is still a lot of research going on into the effects of PED's (Portable Electronic Devices) of all kinds on aircraft systems of all types. There is considerabel circumstantial and anecdotal evidence that GPS's, mobile phones, even CD players can cause interference. They are currently searching for the hard evidence into the above.
There is, therefore, some doubt as to the effects of specific devices. I was always taught that, where flight safety is concerned, "if there is any doubt, then there is no doubt". In the meantime, I am sure people would prefer to be safe than sorry, and therefore would not use PED's without permission.
Mobile phones may not legally be used at all on board an aircraft unless specifically designed for the purpose since all base stations within sight perk up and try to provide a service. Therefore it is possible for one mobile phone to seize up an entire network.
Next, it is conceivable that hijackers or suicide bombers could use information from a handheld GPS to decide exactly where to take action. Therefore some airlines are rather sensitive about this sort of thing.
And finally, it is illegal to use any PED aboard any aircraft if the airline tell you you may not use them. If you disobey a lawful instruction, you are liable for any and all consequences of your action.