Hi Arouet... thx for the detailed summary :)
I don't think it makes a difference.
If by that you mean that they are all functionally equivalent, I will respectfully disagree. I'll tell you where I see the difference and hopefully you can elaborate on your view.
Although I tend to express myself more diplomatically, I would agree with you in principle that the phrase "Consciousness is an illusion" is moronic. This assumes that we're using consciousness in the broad sense of "to have subjective experience" and similar definitions. As is often noted on this forum, the fact that I am conscious is one of the only things I can be absolutely sure of. I have experiences. That is undeniable. Further, consciousness means "to have subjective experience", an illusion is a type of subjective experience. Consciousness is the set, illusion a subset. The set must by definition be greater than the subset.
So the phrase "consciousness is an illusion" is simply nonsensical and denies the undeniable. It is bad reasoning plain and simple and does not reflect well on the person who utters it. It merits criticism in those who advance it.
I hope we can both, agree, that the criticism is only merited if the person actually made the argument. Time and time again I see the accusation made, but it never seems to be accompanied by a direct quote. The closest we see to a citation is a general reference to Dennett's "Consciousness Explained" or the title of Dennett's Ted talk "the Illusion of Consciousness". I've posted about this before: I have looked through those and many other sources. I have yet to find a single quote (with a small caveat, I've seen it once or twice uttered but the accompanying explanation makes it clear that the author really meant something different).
Of course, I could have missed it - after all I can't read and listen to everything! So if you (or anyone) can point out some direct quotes, that might change my opinion and I will stand to be corrected. But if there are none, then I would submit that the allegation should be retracted as it turns from legitimate criticism to misleading rhetoric.
Now, we have plenty of examples of these folk making comments along the lines I quoted above in terms of free will, the hard problem and the sense of self being illusory. If they are functionally equivalent to "consciousness is an illusion" then they would equally paint an unflattering picture of the reasoning skills of these thinkers. The thing is, I can't think of how they can possibly be considered equivalent.
Free will refers to how certain conscious experiences come about. The allegation of illusion refers to the proposition that the feeling (ie: a subjective experience) of our will being free is an illusion. That is, we make choices, we have intention, but they are as a result of either determined or random processes. (There are more nuances of course but I think we can keep it simple for our purposes). The argument may ultimately be demonstrated to be incorrect, but not for the manifestly terrible reasoning set out above. This is a debate that has raged for centuries and probably mellenia. There are detailed, nuanced, often imaginative and carefully reasoned arguments on both sides. Whichever side is correct, I don't think either side can be dismissed out of hand in the way that Consciousness is Illusion can be.
How about the sense of self? This is another one. First of all, it is clear that the sense of self is another subset of the set of conscious experience. There is no logical flaw there. Descartes' "I think, therefore I am" lets us have no doubt as to the fact of our existence, but it gives us no help as to what "I" actually is. I think we probably agree that the nature of the self is currently unsolved. Hypotheses abound, with many conflicting. The illusion being desribed here is the proposition that our sense of self as a single, unitary "thing" is what is illusory. The argument is that the self is not what many people think it is. Right or wrong, we can't figure this out just by thinking about it. The arguments depend on confirming the premises - they can't be discarded out of hand as terribly reasoning in the way that Consc=Illusion can. Great thinkers have wrestled with it and continue to.
Regarding the hard problem, I'm not sure I get what he's saying in that clip. I've heard Dennett talk about the hard problem not really being a problem - maybe that's what he means. Unfortunately the clip doesn't give a lot of context. So maybe we should put this one aside. I think the above makes my point.
The reason it matters is because of its affect on the debate. Lumping them all in serves to lead people to approach these very difficult issues emotionally rather than with careful thought. It convinces people through peer pressure. It's the same tactic used by people like Randi: tainting a valid line of exploration as "woo" which serves to discourage people from looking at it more closely for fear of looking stupid by even engaging it. Sure, it'll influence people's thinking but do we really want to reach our conclusions that way? It doesn't just peer pressure others, it has a similar effect on oneself.
It's important because it serves to increase bias and ingrain US/Them divisions. It reduces open mindedness and limits our thinking. It's important as a case study of a widespread practice. This isn't a partisan issue: other examples are skeptics using 'woo' or dismissing all arguments in favour of the paranormal as being due to "fear of death", or on the other side the use of "pseudoskeptic" or "biological robot".
It's important because it hurts our ability to give ourselves our best chance of figuring all this stuff out. It leads us to reject or accept ideas for the wrong reasons.
That's how I see it. Happy to elaborate further. I'm quite interested in your view.