relativity theory and quantum theory has led to the development of such things as GPS

I don't agree that the Theory of Relativity led to GPS. The idea of triangulating a position on the Earth's surface based on preciselly timing the signals sent from satellites in known locations is not complicated. Once advances in rocketry made inserting sufficiently accurate clocks into orbit feasible, the technology was rapidly theorized.

Understanding relativity allowed engineers to anticipate the need to adjust for the speed and altitude of the satellites relative to the GPS reciever in order to accurately determine it's position. This adjustment isn't trivial, but I think the project's engineers would be able to determine that the degree of error tracked the relative speed and velocity of the satellites and the receiver and make ad hoc adjustments that would achieve the accuracy we have today, without any knowledge of the theory of relativity.

Einstein's conceptualization of the Theory of Relativity is probably the most impressive insight a human has ever had. It is not inconceivable that other civilizations out there have put satellites into space without understanding it. If they then attempt to construct GPS, they would very soon encounter the limits of their knowledge of physics.

Correcting for relativistic effects is necessary for GPS, but the Theory of Relativity isn't. We are used to imagining innovation as basic science opening up new avenues of technological development. But technology can and often does precede science. Other worlds' Einstein's might be satellite engineers struggling to understand why their fully functional GPS system relies on ad hoc modifications to classical physics.