Others in this thread do believe that entropy is a subjective measure, or more precisely a measurement of the information that an observer has about a system instead of a measurement about the state of the system itself. Information theory easily leads to this interpretation, since for example the informational content of a stream of bytes can very much be observer-dependent. For example, a perfectly encrypted stream of all 1s will appear to have very high entropy for anyone who doesn't know the decryption process and key, while in some sense it will be interpreted as a stream with entropy 0 by someone who knows the decryption process and key.
Of course, the example I gave is arguable, since the two observers are not actually observing the same process. One is looking at enc(x), the other is looking at x. They would both agree that enc(x) has high entropy, and x has low entropy. But this same kind of phenomenon doesn't work with physical entropy. A gas is going to burn my hand or not regardless of how well I know its microstates.
As far as I understand it, the original thread was about whether this distinction exists at all. That is, my understanding is that the whole thread is about opposition to the Quanta article's assertion, which suggests that thermodynamic entropy is the same thing as information-theory entropy and that it is not a "physical" property of a system, but a quantity which measures the information that an observer has about said system.
If you already agree that the two are distinct measures, I believe there is no disagreement in the sub-thread.
Is there a concrete physical example where the information-theory definition of entropy conflicts with experiment?