Earlier quoted context omitted.
But relativity explains GPS. And the two theories together explain practically everything to insane levels of precision. The only time they go wrong is when they both operate at once, in a narrow range around black holes or the very earliest universe.
General Relativity doesn’t end just above the atmosphere and quantum mechanics ought to apply to everything, not just experiments. The current microscopic models don’t even attempt to explain how a molecule of water is lighter than the oxygen and two hydrogen atoms that went into making it. Oh sure, we can wave our hands at it and invoke the mass-energy relation from GR, but this doesn’t “pop out” of the Standard Mod…
Your are correct that there is a (strong) conflict between general relativity and quantum field theory, and this is a major problem for theorists, but it does not pose problems for using mass-energy equivalence in quantum field theories (since it comes from SR not GR).
There are real, physical, examples where the GR/QFT conflict is more problematic. For example in quantum physics labs around the world it is possible to put things which have mass in superpositions of being in two different places. This is usually done with very small objects, but it happens. We have absolutely no idea what is happening to space-time when we do this.