About the lack of subjectivity of the states? If we consider any bit of matter (for example a crystal or an ideal gas), the macrostate is completely independent of the observer: it’s just the state in which the law of physics say that bit of matter should be. In an ideal gas it is entirely determined by the pressure and volume, which are anything but subjective. For a crystal it is more complex because we have to account for things like its shape but the reasoning is the same.
Then, the microstates are just accessible states, and this is also dictated by Physics. For example, it is quite easy to see that a crystal has fewer accessible states than a gas (the atoms’ positions are constrained and the velocities are limited to the crystal’s vibration modes). We can calculate the entropy in the experimental conditions within that framework, or in the case of correlated liquids, or amorphous solids, or whatever. But the fact that we can come up with different entropies if we make different hypotheses does not mean that any of these hypotheses is actually valid. If we measure the entropy directly we might have a value that is consistent with several models, or none. The actual entropy is what we observe, not the theoretical scaffolding we use to try to make sense of it. And again, this is not subjective.
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.
"It's [...] not right" (from your first comment), can you give/link a specific physical example? It would be very cool to have a clear counterexample.