I've completed a full year QM course (undergraduate level) and I am left confused on where to draw the line between quantum mechanics theory and its interpretation(s). I would personally like to stick to no interpretation at all, but since I do not know what is interpretation and what isn't, it is extremely hard to stick to this rule. Many introductory books do not mention if they use a particular interpretation at all, and I suspect they do use some interpretation(s) here and there, without any warning nor notice.
From what I have read on the Internet, the "collapse" or "reduction" of the wave function, is part of interpretations of QM. Not all interpretations assume there is even such a thing as a collapse of $\Psi$. Good, that's an easy one.
But what about what $\Psi$ represents for example? I've commonly read that its modulus squared represents the probability density of finding the particle(s) at a particular position(s) and time(s). But does such a description already assume an interpretation?
What about the QM postulates? Is there any interpretation hidden in one or more of these postulates?
I've read several Lubos Motl's posts (here on PSE and on his own blog) and to him (and apparently many others such as John Rennie and Zurek), $\Psi$ is entirely subjective and two observers of the same quantum system need not to use the same $\Psi$ to describe the system. But no mention of any interpretation is ever done. I suspect they use some interpretation to make such claims, but I couldn't get the information from skimming through many books (including one by Zurek called "Quantum theory and Measurement" which is a package of many QM papers and one such paper by London around page 250 seemed to agree with the Motl's description).
I have heard of the "Shut up and calculate!" approach, but I have read on Wikipedia that it's associated to the Copenhagen interpretation. Is that really so?
I have read from the member alephzero that QM works perfectly well without any interpretation. Quoting him:
"Wave function collapse" is not part of QM. It is only part of some interpretations of QM (in particular, the Copenhagen interpretation). The fact that this interpretation is used in a lot of pop-science writing about QM doesn't make it an essential part of QM - to quote David Mermin, "just shut up and calculate!" Note: AFAIK there is no so-called "standard interpretation" of QM - it works perfectly well as a theory of physics with no "interpretation" at all.
My question is, how on Earth do we draw the line between QM theory and its interpretations? The books seem completely blurry in that aspect and almost any other sources I could find too.