First, welcome to FT!

I do not believe that GPS use is any security risk at all, but that does not mean that airline employees will not claim that it is. They tend to claim that anything is a security risk if they do not want you to do it. I have always understood that the "security" reasons of some airlines against GPS use included that they did not want someone to know exactly where the aircraft was so they could do something nefarious at a particular place/time.