The incompatibility of QFT and GR is a theoretical incompatibility. Practically, however, GR is perfectly compatible with quantum mechanics right to the limit of strong gravity, which can only find inside black hole event horizons (and in particular at and very near the singularity), and in the very early universe.
In GR terms, strong gravity is where the uncertainty in position of field quanta sources an impossible gravitational field; this is only measurable when the energy-density is non-negligible and that requires enormous quantum numbers. In quantum field theory terms, the (general, not just electromagnetic) charge of a particle and its energy are separate quantities except for the gravitational charge of a particle, which is its energy. Because the gravitational interaction is so weak, this only matters when particle energies are very high (on Feynman diagrams, this means more than one loop of gravitons; while gravitons are massless they do carry momentum, and thus have energy, and thus gravitational charge).
The clocks in GPS satellites all rely on quantum effects, and those effects that run faster further from the Earth than they did closer to the Earth prior to launch. GNSS applications, as well as atomic clocks on spacecraft scattered around the solar system, are ongoing tests of the validity of this prediction of GR.
It is precisely because General Relativity is an effective field theory (in the Kenneth G Wilson sense of effective) in all presently accessible regimes, and has so far survived every test -- direct and indirect -- that it is extremely hard to arrive at an explanation for the effects of gravity pointing the wrong way other than non-luminous, transparent matter rather than a different theory of gravity.
In GR terms, strong gravity is where the uncertainty in position of field quanta sources an impossible gravitational field; this is only measurable when the energy-density is non-negligible and that requires enormous quantum numbers. In quantum field theory terms, the (general, not just electromagnetic) charge of a particle and its energy are separate quantities except for the gravitational charge of a particle, which is its energy. Because the gravitational interaction is so weak, this only matters when particle energies are very high (on Feynman diagrams, this means more than one loop of gravitons; while gravitons are massless they do carry momentum, and thus have energy, and thus gravitational charge).
The clocks in GPS satellites all rely on quantum effects, and those effects that run faster further from the Earth than they did closer to the Earth prior to launch. GNSS applications, as well as atomic clocks on spacecraft scattered around the solar system, are ongoing tests of the validity of this prediction of GR.
It is precisely because General Relativity is an effective field theory (in the Kenneth G Wilson sense of effective) in all presently accessible regimes, and has so far survived every test -- direct and indirect -- that it is extremely hard to arrive at an explanation for the effects of gravity pointing the wrong way other than non-luminous, transparent matter rather than a different theory of gravity.