The OP asked it..so..here we go...
In the science, physics, philosophy (philosophy is the father/parent of science), psychology, etc...meaning in the peak of all of this, in the true meaning of all of this...'objectivity' does not really exist.
the only thing that exists is a subjective reality experience. Objectivity, the concept of it, the idea of it, the expression of it, pours entirely out of a subjective experience. in the real world of fundamentals in all we know, at the heights of academia, definition of reality, research, all of it......there's not one single objective consideration that can be proven to be real, including any ideas on 'reality'.
The renaissance people of the past, the multi-skilled masters of the past, came up with the idea of objectivity to help themselves and others try and understand what this place is, and then be able to move the monkey aspects of the body around, but really -- that's about all she wrote.
This, codified and categorized, labelled, defined, etc..this is part of the core of the enlightenment in western society and what become the rigors of western science.
This was considered defined, to some extent, to prevent being lost in circularity (full knowing is not available), by Descartes in the over-simplified axiom (old school meme) of popularity, in the saying of "I think, therefore I am".
This is not the base of the question, or the base of all the considerations, nor is it he final backstop of research and investigation, which is the dangerous part (calling it complete while it isn't--rookie mistakes).
It (the Descartes axiom/meme) brick walls proper research into reality and stops it cold. Which is anti- science, and is generally used incorrectly by people (that fundamental rookie mistake). It is the dividing point between engineers and dilettantes. the central bulk of the IQ and awareness curve-- running around in the box, doing it's social thing.
True actual full on scientists, who are the people who really attempt to unfold this complex and totally unsolved reality question, they look at the whole equation which includes their own unreality..as they HAVE to, or their musing is meaningless and rudderless.
In other words, at the peak of all meaning and intent in science, it is still, beyond a shadow of a doubt.. turtles, all the way down.
Never forget this, and don't get caught up in the idea that your expression through this thing we call a slightly evolved monkey body - actually means anything..... outside of it being a subjective experience in a non-inclusive reality (incomplete, therefore incorrect and destined to FAIL, if attempting to answer truly difficult questions) -- in a meat monkey body.
Which is how one gets to situations (one of identical thousands if you look) where someone like Elon Musk, is totally correct, when he says there is very scant chance at all (ie, billions to one), that this impression of reality is an actual base reality. That this is a subjective experience, created on a skin or skein of some dimensional sort, and is information/differential or data based in some way or another.
Max Planck, the father of quantum science said basically the same thing (again, one instance in thousands, if you look), where he called it an 'information field'. Every thing we know, in the cutting edge of all sciences, says the same thing. You are a thought form in a meat box of undefined parameters, and nothing is real - by the very methods of all possible forms of measurement. Physics in all it's musing and works--totally agrees with this premise. No choice, it is evident in all things for all talented and determined explorers.
Descartes statement is misapplied (i think, therefore i am), and this allowed for the creation of engineering based science, but it is in no way a full representation of the real world. The bulk numbers who do not understand this Descartesian separation point in thinking... do not make their opinion in these matters 'real', if they disagree. It just makes them incomplete and incorrect.
If they get angry about this, avoid them, avoid bringing the question up, when around them, and connecting with them, if one values their monkey meat box of a vehicle of experiencing this reality.
THIS, all of the above, is why, in the physics department and all of it's subdivisions into science and training and academia.. that all of the professors, if pushed and asked, will tell you that there is no such thing as a fact, and all is theory.
We get all these angry 'fact mongers' on forums, everywhere, on all forums..who don't understand this ..... and attack, demanding their own self security be reflected by me, into them... a thing that.. which ultimately...cannot and does not exist.
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So, very very importantly, here...we gotta keep this straight (it is the op itself)..it is quite critical to the subject at hand: objectivity is a thought experiment - nothing more.
Where, if we go forward, in proper understanding of these critical points (stop windmilling and falling through an undefined blackness, angry and seeking hand-grips for your monkey), you'll have less stress in your life.