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There is a problem, not just among laymen, but also among academics, to continually conflate contextuality with subjectivity.
If I ask you the best music genre, and you ask me the best music genre, we will likely give different answers, because the question is subjective. It depends upon the subject and there is no "objectively" best music genre in the world. If I ask you the velocity of an object, and you ask me the velocity, it is conceivable we might give different answers if we are both perceiving it in two different reference frames. Is that because velocity is subjective? That it is all in our heads and just a personal opinion?
I find this hard to believe, because you can conduct an experiment where two observers use radar guns to measure the velocity of the object they are perceiving, and you can later compare them and see that the radar gun does indeed agree that the velocity was different. If it was purely subjective, why would a purely mechanical device like a radar gun also record the difference, which is not a conscious observer or a subject at all?
I believe that velocity can ontologically differ between observers. Meaning, it is part of objective reality that it differs. But this difference is not because they are observers. If the observers observed the same object in the same frame of reference they would perceive it at the same velocity. The difference is not reducible to them being observers, so calling it "observer-dependent" is misleading. The difference goes beyond them being observers and into objective reality: that they perceive the object in different measurement contexts.
This is what I mean by the distinction between contextuality and subjectivity. Some properties of then natural world really do ontologically realize themselves differently in objective reality depending upon the context of their realization.
Basically, what these academics do who claim quantum mechanics disproves objective reality is that they conflate subjectivity to contextuality and then demonstrate that two observers can give a different description of the same system in principle in quantum theory, and then conclude that this means there is no objective reality because the description of the quantum system must be subjective as it differs between the two observers. But, again, that does not follow. One can just interpret the difference as context-dependent rather than observer-dependent and then there is no trouble interpreting it as a physical theory of the natural world independent of the observer. It is just not independent of context.
There is in fact a whole philosophical school called contextual realism based on Wittgensteinian philosophy and originated by the French philosopher Jocelyn Benoist that argues that much of the confusion in philosophy (such as the "hard problem") ultimately has its origins is continually confusing the contextual for the subjective and if the distinction is adhered to clearly from the get-go then the issue goes away. The physicist Francois-Igor Pris has written extensively on the relationship between this philosophical school and interpretative problems in quantum mechanics.
The logic of quantum theory does allow for two different observers to give different descriptions of the same system, but (1) the differences are never empirically relevant as the theory also predicts that if they were to become empirically relevant they would both agree on what they would both perceive, and (2) the theory predicts those deviations in the description, kind of like how Galilean relativity predicts that two observers will record different velocities in different frames of reference by using a Galilean transformation.
The fact that theory predicts these differences (in point #2) makes it hardly subjective, as the deviations are predicted by the objective theory, and they are always consistent with one another (in point #1).