Special pleading. You wouldn't accept any claim that an event from a broad category of events with a total probability indistinguishable from 0 had happened by quantum happenstance if it wasn't an alleged miracle, so you shouldn't accept a claim that an event with a probability indistinguishable from 0 happened by quantum happenstance if it is an alleged miracle.

"Your honor, it's technically possible, albeit with a probability indistinguishable from 0, that the video of my client committing the crime was the result of random quantum fluctuations in the film. I move that the charges be dismissed with prejudice!"

Moreover: The old standby for dismissing evidence - "everyone involved in measurement was lying or had a similar hallucination!" - is much more likely by so many orders of magnitude than any macroscopic object doing intact quantum teleportation, that the contribution of quantum mechanics to the probability can be dismissed anyway. If you're going to advance a bad argument, at least advance the stronger bad argument.

(In point of fact, the probability that quantum mechanics is irrelevant because everybody involved in figuring out quantum mechanics is, incredibly, having the same kind of hallucination, or that they are all participating in the same vast, incredibly improbable conspiracy, is itself many, many, orders of magnitude larger than the quantum-mechanical probability of macroscopic quantum teleportation. The model defeats itself.)

Maybe more to the point: Shouldn't we expect that when Nature acts in accordance with her most fundamental ordering principles, that her actions should appear compatible with, yet inexplicable by, the most fundamental principles identifiable by us? Just as quantum mechanics is itself compatible with, yet inexplicable by, the Newtonian kinematics of macroscopic bodies?

Rightly or wrongly, theists tend to believe that God is the fundamental ordering principle of the universe. Phenomena which are compatible with the most advanced models of physics, but which no physicist could have predicted, seems to be exactly what a good theistic model would predict.

doesn’t the modern theory of quantum mechanics imply that even these things are possible just at an absurdly low probability?

Yes (with some caveats for conservation laws), but...

If so, if events like that did happen, could we still be justified in saying that there’s a natural explanation for this?

Yes, but...

would events like the Red Sea parting be a violation of a scientific law

Not necessarily, but...

and thus count as a miracle and potential evidence for divine intervention or not?

...but there's no such "and thus" to be inferred.

You wouldn't accept any claim that an event from a broad category of events with a total probability indistinguishable from 0 had happened by quantum happenstance if it wasn't an alleged miracle, so you shouldn't accept a claim that an event with a probability indistinguishable from 0 happened by quantum happenstance if it is an alleged miracle. See: special pleading.

Moreover: The old standby for dismissing evidence - "everyone involved in measurement was lying or had a similar hallucination!" - is much more likely by so many orders of magnitude than any macroscopic object doing intact quantum teleportation, that the contribution of quantum mechanics to the probability can be dismissed anyway. If you're going to advance a bad argument, at least advance the stronger bad argument.

(In point of fact, the probability that quantum mechanics is irrelevant because everybody involved in figuring out quantum mechanics is, incredibly, having the same kind of hallucination, or that they are all participating in the same vast, incredibly improbable conspiracy, is itself many, many, orders of magnitude larger than the quantum-mechanical probability of macroscopic quantum teleportation. The model defeats itself.)

Maybe more to the point: Shouldn't we expect that when Nature acts in accordance with her most fundamental ordering principles, that her actions should appear compatible with, yet inexplicable by, the most fundamental principles identifiable by us? Just as quantum mechanics is itself compatible with, yet inexplicable by, the Newtonian kinematics of macroscopic bodies?

Rightly or wrongly, theists tend to believe that God is the fundamental ordering principle of the universe. Phenomena which are compatible with the most advanced models of physics, but which no physicist could have predicted, seems to be exactly what a good theistic model would predict.