Let's say that I have a mobile app that tracks the user and saves his GPS coordinates locally only on a mobile device so that he can check where he was. The mobile application does not send this data to any server. Does GDPR affect me and my app in any way? Do I need for example to change my app in such way that it encrypts that personal GPS data on the device? Or GDPR has no influence on my app as I as a person do not have any access to that data?
No. As long as you don't see and have no means to access this data, but it is under the control of the user at all times, you are neither the controller or the processor of this personal data, and the GDPR does not apply to you.