The fundamental red herring of quantum gravity:
Only the general relativistic time is at odds with quantum mechanics; the special relativistic time is compatible and quantum mechanics and special relativity successfully work together combined in quantum field theory.
This red herring is so idiotic that even Einsteinians often contradict it, explicitly or implicitly:
"The effort to unify quantum mechanics and general relativity means reconciling totally different notions of time. In quantum mechanics, time is universal and absolute; its steady ticks dictate the evolving entanglements between particles. But in general relativity (Albert Einstein's theory of gravity), time is relative and dynamical, a dimension that's inextricably interwoven with directions X, Y and Z into a four-dimensional "space-time" fabric." x
"In quantum theory, a "master clock" ticks away somewhere in the universe, measuring out all processes. But in Einstein's relativity, time is distorted by motion and gravity, so clocks don't necessarily agree on how it is passing - meaning any master clock must, somewhat implausibly, be outside the universe."
Perimeter Institute: "Quantum mechanics has one thing, time, which is absolute. But general relativity tells us that space and time are both dynamical so there is a big contradiction there. So the question is, can quantum gravity be formulated in a context where quantum mechanics still has absolute time?"
"In Einstein's general theory of relativity, time depends locally on gravity; in standard quantum theory, time is global – all clocks "tick" uniformly."
"One one hand, time in quantum mechanics is a Newtonian time, i.e., an absolute time. In fact, the two main methods of quantization, namely, canonical quantization method due to Dirac and Feynman's path integral method are based on classical constraints which become operators annihilating the physical states, and on the sum over all possible classical trajectories, respectively. Therefore, both quantization methods rely on the Newton global and absolute time. [...] The transition to (special) relativistic quantum field theories can be realized by replacing the unique absolute Newtonian time by a set of timelike parameters associated to the naturally distinguished family of relativistic inertial frames."
"In quantum mechanics, time is absolute. The parameter occurring in the Schrödinger equation has been directly inherited from Newtonian mechanics and is not turned into an operator. In quantum field theory, time by itself is no longer absolute, but the four-dimensional spacetime is; it constitutes the fixed background structure on which the dynamical fields act. GR is of a very different nature. According to the Einstein equations (2), spacetime is dynamical, acting in a complicated manner with energy momentum of matter and with itself. The concepts of time (spacetime) in quantum theory and GR are thus drastically different and cannot both be fundamentally true."