I would have added a comment to @JamesHam's answer but I don't have the rep.
Long story short, Your GPS on your phone is receive only. Yes your antenna will generate some field but I doubt it is much stronger when the phone is on than when it off. (However, antenna and interference were not my area of expertise.)
GPS signals travel at the speed of light. Even plane at top speed is still very close to stationary by comparison to the speed of light. Any issues you have with regards to GPS at speed have to do with your phone's hardware/software.
As far as the safety issue is concerned... It is a myth. Period.
While this is not my area of expertise a little simple logic goes a long way. Consider that your plane is awash in signals at a lot of frequencies while it is on the ground and at landing and takeoff (the most dangerous times). Signals from cell towers, FM and AM radio stations, GPS, DirecTv, lightning, etc. All of these sources bathe the airplane in EM waves across a slew of frequencies. Most bathe airplane with much more power than your phone can. Additionally, every wire with electricity in the airplane puts out an EM signal as well.
Another logic argument, there are approx 200+ people on every major flight in the US. If only 1% forget to turn off our phone that means there are at least 2 people on every flight with their phone's on the entire flight. EM interference happens over the course of less than a second so every hr of flight time represents at least 3600 discrete opportunities for EM interference per operational phone. How many flights crash every day?
Any modern aircraft is digital not analog. So interference due to EM can really only cause a flipped bit or a few. As far as a sweet spot in frequencies is concerned the most likely culprit for interference will come from other aircraft systems that sample and process data at the same frequency as the system being interfered with.
But so what? Every sensor man has ever created will create the occasional bad data point. Planes, satellites, etc all have to be robust to a few bad data points. So every computer that consumes sensor data on airplane has filters built in to it specifically to deal with a short series of bad data points.
Specifically the navigation system is usually blamed when the FAA or someone says EM interference brought that plane down. They then go about telling you how impossible it would be to prove it. So ... why do we believe them?
The navigation system in particular is built in such a way as to cope with missing and bad data. Typically the nav system uses some combination of multiple attitude, acceleration, velocity, and position sensors operating at different update frequencies. GPS is often only updated once a second while gyros and accelerators are updated sometimes 1000s of times a second. Then there is a propagator (or estimator) that calculates the aircraft's position, velocity, and attitude in between GPS updates using the faster sensor data. All of that sensor data is filtered so that the occasional garbage data point (which every sensor ever built generates) doesn't cause the aircraft to behave wildly, unpredictably, and sometimes fatally.
The nav system is often blamed because it is all software and sensors. The engine can't spin up or slow down fast enough for a few spurious data points to cause issues. Neither could the controls surfaces (flaps, ailerons, etc). A spurious blip in the radio or radar by themselves doesn't cause an aircraft to go down. So by deduction it can only be the nav system becoming confused by bad data. Except every modern nav system is inherently robust to noise on the sensor data and the larger the error is in the spurious noisy data the easier it gets filtered out.
Oh, and every single computer system on an aircraft is shielded against EM interference.
EM interference is a boogey man the FAA uses when they don't have an answer. It is reproduce-able in a lab in just the right setting. But the aircraft would never have gotten off the ground if it were sensitive enough to crash due to your cell phone or even 200 cell phones simultaneously in use on board.