No one has ever denied experience, that I know of. What's being questioned, with regards to things like dreams, are their objective realities.
I think you'll find that objective realities are a part of subjective realities. They are merely agreed upon truths, which are in fact relative to the person, or group holding them as truth. The "myth of the given", is the idea that reality is laying around out there for us to discover and as it is without any subjective influences in its understanding. But this has been shown to be fallacious, hence why it's called the myth of the given, or the myth of the pre-given world as another way it's stated. The observer is always as much a part of that understanding, and the scientific method does not get us beyond that, because the empiric-analytic approach will always color what it observes with its own assumptions. It becomes in this sense part of the "consensus reality" or consensus trance, where what is seen is part of the sets of eyes looking at it. There is no "in itself" to be understood without the observer himself as part of it.
And all this is understood from the postmodernist perspective, which just happens to come closer to what mystics have been saying all along.
I'll get to this later.
Experiences are all relative and subjective, as I'm sure almost everyone would agree. But when asked whether or not that experience can manifest itself without the subjective cognition of the dreamer, the answer has to be no.
The experience can be very real, subjectively. And the fact that a cognizant being intrapersonally created a subjective experience is also without question. But the Experience itself is not manifest objective reality.
Exactly. No matter what manifests itself in the world, it has us as observer and interpreter as part of it. All that is happening in dream states is the imagination putting mental objects upon phenomena. All that happens in the waking state is the imagination putting mental objects created through the imagination upon phenomena.
Here's what happens in the waking state, and follow this carefully. The individual has an experience. That experience is then instantly split out into two parts in the mind of the perceiver. It is split into two questions; "what was that?" and "what does it mean?". That is the subject/object split. "What was that", is a question of what something is outside of yourself, its objective truth. "What does it mean", is the subjective question. What does it mean to me personally on the inside? Is it a threat, is it helpful, is it something I want, what are its implications to me. This same process occurs at the group level as well, where the group collectively encounters phenomena and asks its objective meaning (science and observation), and it subjective meanings (philosophy and religion, the value spheres).
Now, when it comes to "objective reality", regardless of the power of the tools used to look at phenomena, you still have all the relative frameworks that the individual, or by extension the group, the collective mutually uses - the same set of lenses each looks through. That set of lenses has and continues to change, and to mistake the enormous successes with a particular set of lenses with having achieved a true escape velocity in order to be able to break free from the gravity of the subjective is itself, a subjective hope, desire, and dream inserting itself as a belief. Logically it can be shown that even the scientific method, as powerful as it is in united a common approach, is itself a bit of an illusion of mind, to say the least. It asks only questions in selective areas it feels it can answer, it deals only with the most stable systems such as physics, etc.
On the other hand you have phenomenologists who think if you can look sufficiently into the experience itself it will reveal its true nature. This is the opposite side of the street between materialism and phenomenology who seeks to make reality the subjective experience itself. But this too has been shown to lack an understanding of the role of cultural, as well as developmental influences in how one perceives truth and reality. This too cannot escape the gravity of the influences of the structures of culture, or in this case the objective influence on the subjective experience. Cultural phenomena is in a sense an object to the individual, just like the material word is an object, outside the individual.
Yet it all interacts with each other. Ultimate reality cannot be understood by looking outside the subject to the material world using science. Despite the enormous understandings that have opened to us, it can never escape the subjective or the culture, the group, the inter-subjective influences. It is still relative, not ultimate, and can never be understood excluding the subjective. Likewise Ultimate reality cannot be understood by looking solely at subjective experience of reality. It too is relative to the influences of culture, language, and developmental stages.
So where does all this leave us? Enter here the mystic. When you drop all the lenses of subject and object, drop all relative truths, drop all objects of thought, and simply rest in Being itself, "mindlessly", as it were, it experiences 'being itself', which is all phenomena, all objects. They all simply arise and fall within Awareness itself. They are not themselves inherently true. A person is not a person, but everything in the universe. Even this can be understood when looking at what science shows. We are atoms and molecules. We both exist and do not exist. And what is more is it is realized in the state of being itself, before all divisions of subject and object. But in reality, this realization is the nondual realization, that arises after all phenomena dissolves into Emptiness and your rest in this Nothingness. Understanding that, the entire parade of phenomena is a world of unfolding realities. Including the modern revolution of science. The manifest world, Ultimate Reality, includes all relative realities, as well as the Emptiness of everything itself. It is neither this nor that, not not-that but this, but it is Nothing and Everything. It is a dance of notes played by evolving individuals on the very strings that vibrate in everything that exists and does not exist.
Ultimate Truth does not deny relative truths. It does not deny the subjective, nor deny the objective. It embraces everythings and holds nothing. It is objective reality and subjective reality at once within itself.