The hard problem of consciousness basically says that we can't prove identity or causation. We can demonstrate an overwhelmingly strong correlation between consciousness and the brain, such that they seem to be one and the same in every conceivable way, but we can never get conclusive proof that they definitely ARE one and the same, and we can never get conclusive proof that something definitely causes something else.
But if one applies this standard consistently, one would have to reject or perverse most of our understanding of reality.
- How do you know that physical objects bend spacetime - it could be some magical force that exists alongside every object, which is actually the thing bending spacetime.
- How do you know that any given electrical component actually does what it seems to do - it could be some magical force that exists alongside every such component, which is actually the thing transmitting electricity or whatever.
This is what dualism does: it says that we can't definitively know that the brain actually does what it seems to do, and that the effects observed are actually the result of some magical force that exists alongside every brain.
The hard problem of consciousness may as well just be called the hard problem of identity or causation. The most reasonable response to that is: Interesting note. Anyway. Let's continue with the most reasonable interpretation that this is identity and causation. It would not be a particularly reasonable response to say that therefore magical forces exist.
In any case, you ask about psychedelics. These absolutely strengthens the correlation, and makes dualism that much less plausible. But it doesn't refute the problem above, because nothing can refute that problem - it's unfalsifiable.
Eternally repeated (frequently refuted) arguments against physicalism
Under the causal closure assumption of physicalism
Physicalism makes no such assumption. Physicalism just means we don't posit explanations that are magical invisible forces or entities which we can't reliably observe, directly or indirectly.
The only "causal closure assumption" one can really get from the above is that non-existent things (which seems to be all proposed "non-physical" things) can't have causal effects. If you want to justify the existence of non-physical things, and justify how we can reliably know about their causal effects... get to it then. Good luck though, given that people have been trying and failing at that, for thousands of years.
See also: my answers on the questionable distinction between "physical" and "non-physical".
phenomenal experience does not seem to have the location, energy, mass, or other properties that seem to be core to being "physical"
This seems to just outright presuppose dualism and deny physicalism. And then it tries to present this presupposition as an argument for the thing it's presupposing.
Under physicalism, the "location, energy, mass, or other properties" of phenomenal experiences is (a) in your brain, (b) the energy required by your brain, (c) the mass of electrical activity and chemicals in your brain and/or your brain itself, and (d) other properties of electrical activity and chemicals in your brain and/or your brain itself.
The primary strategy pursued by physicalists is to make identity claims ... Neural identity theory is refuted by observation
This is demonstrably false. The plurality view, at least among philosophers, is functionalism. Identity theory is close to a third as popular. Meanwhile, scientists (the people actually getting their hands dirty in trying to understand reality) are reductive physicalists in practice, whether they adopt that label or not (more on that below).
Identity theory (at least in the form presented here) is a poor perversion of reductive physicalism. It tries to turn reductive physicalism into a strict categorisation of reality, despite the fact that it's well-demonstrated that reality fails to fit neatly into our attempts categorise it. This is comparable to pointing to someone saying each animal is a particular fixed "type", and then saying science is "refuted" by the fact that groups of animals change from one "type" to another across generations. The former is a naïve understanding of biological species, and the latter is an even more naïve (at best) attempt to say animals exist magically because the afore-mentioned naïve understanding clearly doesn't reflect our scientific understanding of species.
Reductive physicalism is science (I mean ALL of science, but also neuroscience in particular). It's the practice of trying to "reduce" some observation to some combination of forces and models and particles and such. And "physicalism" means we don't posit explanations that are magical invisible forces or entities which we can't reliably observe, directly or indirectly. Dualism is such invisible magic, whereas we have reduced consciousness significantly to neural processes. Related: my answer on whether reductive physicalism has been falsified.
Dualists seem to shy away from addressing reductive physicalism. I wonder if that has something to do with it being the foundation of all reliable knowledge of reality, as well as a whole lot of reliable knowledge about the brain and consciousness.
The second identity claimed was a functional identity ... it makes physicalism a dualist ontology ... it too is falsified by test
Functionalism says "what makes something a mental state of a particular type does not depend on its internal constitution, but rather on the way it functions, or the role it plays, in the system of which it is a part".
Maybe there exists a version of this which says that mental states are themselves made up of these functions, that this is their fundamental nature. This is what the other answer is addressing, but it seems by far the more absurd interpretation of functionalism.
The more reasonable interpretation and view of functionalism, in my opinion, is that it posits nothing about the fundamental nature of consciousness. It would be a lot like the "shut up and calculate" in quantum mechanics: we don't need to know which neurons are firing to classify something as pain or joy or whatever. I don't have much of an issue with that, and it's basically what psychology does. It's pragmatic. It certainly isn't dualism, and it certainly hasn't been falsified - I can't figure out how one could even conceptually falsify the idea of classifying neural states by their function. It's merely a useful way to group things, it's not a truth claim.