Actually, Newtonian gravity can be added to QM and work perfectly well. It's GR gravity that doesn't work with QM, especially if you try to model very high curvature like you'd get near a black hole.
Quantum Electro-Dynamics (QED) is the application of Special Relativity (non-accelerating frames of reference, i.e. moving at a constant speed) to Electromagnetism. Thus, the issue is with applying accelerating frames of reference (the General in GR) to QM.
Quantum Electro-Dynamics (QED) is the application of Special Relativity (non-accelerating frames of reference, i.e. moving at a constant speed) to Electromagnetism. Thus, the issue is with applying accelerating frames of reference (the General in GR) to QM.