"Airplane mode" does not disable GPS... is it safe to use GPS in flight?
theoretically? GPS IS receive only. There's no way to talk to the GPS satellite network except using the big antennas of the network owners (the US DoD) and the communications are no doubt heavily encrypted.

Now, does that mean it's "safe" for aircraft electronics. Any receiving antenna does have an EM field around it, so if you believe the myth that those electronics are so sensitive and easy to jam that any EM field at all causes them to malfunction the answer is an obvious NO.
But that myth is just that, a myth. If they were so sensitive, that old walkman you were using in the 1980s during flights would have brought down that aircraft. Because not only do antennas have EM fields around them, any electrical device that's turned on has one (in fact any electrical cable with a current flowing through it has one, including the headphone cord for the in flight entertainment system).
And that GPS system in your cellphone uses a lot less power than that walkman, has a far weaker field surrounding it.

Of course it's theoretically possible that a strong enough EM field might interfere with the electronics in an aircraft, but then to you'd need just the right signal. Which would indicate you need intent (or incredible bad luck)!

Effectively the GPS in your cellphone is a lower powered version of the GPS receiver in the belly of the aircraft, which has its own antenna (which no doubt has a similar field around it, but of higher strength).