You appear to be confusing special relativity and general relativity. Mass-energy equivalence pops out of special relativity, and is part of general relativity because GR extends SR. Another class of theories which extend special relativity are (relativistic) quantum field theories. These also have mass-energy equivalence baked into them because they contain special relativity.
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.
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.