It's of no relevance to MOND, at least none that I can see.
MOND gives a different scaling relation, and is therefore contradicting general relativity. Its goal is to explain the effects we associate with dark matter, without the need for dark matter.
General relativity is (we are pretty sure) inconsistent with quantum field theory. String theory tries to fix the issue by replacing the particles in field theory with strings. Oppenheim is trying to fix it by putting general relativity as a classical phenomenon that lives "outside" of quantum field theory.
They're trying to solve different problems. And, Oppenheim's classical gravity picture could be used just as well with MOND instead of standard general relativity, if that's what you wanted.
MOND is getting less popular every year as evidence for dark matter piles up. The Bullet Cluster is a particular instance where we can actually "see" the dark matter flying around, in a way MOND couldn't hope to explain. LIGO has also given us a lot of confidence we have the right theory of gravity, at least up to the quantum scale.
(I went to a talk by Oppenheim author a couple weeks ago on this topic.) The idea is that gravity, as a force, only operates classically. More precisely: there is a classical state describing the curvature of space time, and then a quantum state describing the configuration of particles on that spacetime. But then, that quantum state needs to affect the classical state again (mass bends space), which would usually lead to the classical half becoming quantum and entangled with the other half.
You can keep the classical half (the shape of spacetime) classical, if the effect of the quantum part is partially stochastic. There's a minimum amount of random noise you need for it to be mathematically consistent. So, you set up an experiment where a particle is acting on another via gravity. There's a quantity of noise you should expect to see in the gravitational force.
"Inertial Mass=Gravitational Mass" now only holds on average. The gravitational mass will effectively have a Brownian noise term added in.
MOND gives a different scaling relation, and is therefore contradicting general relativity. Its goal is to explain the effects we associate with dark matter, without the need for dark matter.
General relativity is (we are pretty sure) inconsistent with quantum field theory. String theory tries to fix the issue by replacing the particles in field theory with strings. Oppenheim is trying to fix it by putting general relativity as a classical phenomenon that lives "outside" of quantum field theory.
They're trying to solve different problems. And, Oppenheim's classical gravity picture could be used just as well with MOND instead of standard general relativity, if that's what you wanted.
MOND is getting less popular every year as evidence for dark matter piles up. The Bullet Cluster is a particular instance where we can actually "see" the dark matter flying around, in a way MOND couldn't hope to explain. LIGO has also given us a lot of confidence we have the right theory of gravity, at least up to the quantum scale.