NIMBUS is spot on with his answer.
Any item that emits EMP [including your computer etc.] - Yes they must if they use any form of AC, has the potential to propogate electromagnetic energy across any 'close' wiring. How close - Back to the piece of string theory.
[pure electronics fundamentals really].
DO you know what a 'local oscillator' is? - Any Transmitter AND Receiver has one - therefore they are all transmitters of sort - albeit low power.
Any pure DC powered device emits another form of EMP [Mainly Magnetic Flux] - Minute amounts of which could be sufficient enough to cause wiring to become antennae - or worse, become an oscillator should the wiring within close proximity possess the right amount of shielding [to form capacitance]. Capacitance and Coil [Magnetic] = Oscillator=Transmitter
Put your computer next to your clock radio one day and enjoy the interfenence.
The Big aircraft and Avionics companies go to great lengths to create AIRWORTHY bits of Kit. They include trials of EMP and 'leaks' of EMP. - At great cost.
Of course some shielding and 'localised' effets of various areas of the airframe must be considered, and flight trials and test flights attempt to identify vulnerable spots in order to provide maximum shielding.
Those video screens and in flight entertainment systems dont come cheap. They too will have gone thru extensive AIRWORTHINESS acceptance procedure and protocols
You should see the vast procedures associated with re-wiring any component - especially those with the older compass systems that actually still use Flux Valves.
Whilst you may say that 'nothing has happened in the past' when I used my phone while airborne, can you GUARANTEE that it will not create an EMP problem that you are un-aware of?
As to the GPS - It would be DC powered, but must contain some ofrm of AC oscillator to receive. It is unlikely to cause any problems, but can you guarantee it without some form of Documented Flight Trial or Test Schedule.
Flight Safety is not a gamble.