Having skimmed through the thread, I think it is clear that there is no singular, correct answer - because of the nature of the question and the term involved, which has no clear or specific definition.
I think there are multiple good answers - including many in this thread. I think there are three basic answers, each of which has variations:
- D&D before Dragonlance (OD&D, B/X, early AD&D)
- TSR D&D (the above plus 2E, or anything pre-3E)
- A style or attitude of play (thus including OSR)
Etc. None of the above are "wrong" - all just emphasize different elements of the term "old school" and yield different, but related, results.
I want to say something about that third one, though - or at least extrapolate from it. I don't think anyone has mentioned the fact that the term "old school" is used in a lot of different contexts that have nothing to do with D&D. When people say someone is "old school," it generally means they do things in a way that is no longer popular or widely done. Actually, Urban Dictionary has a decent definition that comes up:
"Anything that is from an earlier era and looked upon with high regard or respect. Can be used to refer to music, clothing, language, or anything really."
I didn't consider the regard/respect part, but I think it generally applies. When we say someone or something is "old school," it generally has positive connotations, like they do something that is no longer done, but has its own charms that may have been lost. For instance, vinyl records or fountain pens or mechanical watches. People generally don't use the term "old school" in the mocking manner that, say, my 13-year old daughter has when she calls me a Boomer (even though I've tried to clarify the difference between a Boomer and Gen Xer!).
That said, I think there's an important distinction to be made between something that is from a specific era, and something that is a re-envisioning of it. Compare an actual 80s movie to Stranger Things. Or a 1970s Funkadelic album vs a modern group of Brooklyn hipsters (or, say, Vulfpeck). This isn't a value judgment either way, but there are different qualities involved. In fact, one could argue that the best re-envisionings are equal or even superior to the originals.
That said, sometimes older things are actually measurably superior, or at least different in a way that is no longer present today, and thus offering qualities that have been "lost." Take fountain pens, for instance. Due to changes in metallurgy and manufacturing over the decades, certain vintage nibs have qualities that are no longer present in modern pens - and perhaps not even possible to re-create. This is why certain fountain pen users are always on the hunt for certain vintage pens, such as the so-called "wet noodle" nibs that modern pen makers haven't quite been able to re-create.
Back to D&D and the style/attitude element, I think another angle on "old school" that hasn't been mentioned is the degree to which the game and fantasy experience relates to reality. An old school approach to D&D sees the D&D world as its own thing - it isn't a reflection of the real world or a context to play out socio-cultural-political dynamics. The game is not analyzed for how it relates to various real world issues - everything within it is what it is, regardless of what connections people decide to make. Or to put it another way, the connections aren't intrinsic aspects of the thing itself. Bugbears are just bugbears - how we choose to interpret or analyze them is separate from the actual bugbear itself - that is, within the context of D&D Land.
Now this isn't quite the same as other definitions of old school, but I think has overlap and is part of the matrix of perspectives that can be applied (and thus either a subset of the third category--style/attitude--or even a fourth category from the three above: the way the D&D world is understood in relationship to the real world).