If we can agree that quantum phenomenon apply to the matter that comprises our neurology then it is a given that quantum behavior is an element of the environment in which our neurology has evolved. Being an intrinsic property, isolating conscious activity from that inherent dynamic requires fully encompassing its behavior in such a way as to sufficiently capture and nullify these characteristics. Barring achieving that effect, we are left with a situation in which quantum phenomenon plays some role in the way our neurology and by that our consciousness works. Frankly, the non sequitor is in thinking that quantum theory DOESN’T play a role in consciousness.
The most substantial fallacy here however is in all this trite search for a silver bullet, the “QUANTUM PHYSICS WILL EXPLAIN MY SOUL” mysticism some seem to embrace. It’s one a piece of a bigger puzzle; there will never be a simple answer at which we can point to and declare “That is I”. Still, why do rational people presume quantum mechanical inclusion as a factor in consciousness? It’s because quantum theory is EXTREMELY useful for explaining how the computationally complex aspects of our cognition are capable of operating; probabilistic computation makes almost trivial types of tasks which are FAR beyond our binary computational approaches. Tasks which are critical to simulating reality in a non-polar universe. If we have an evolutionary system developing with access to the components useful for developing a computational advantage that increases survivability, Occam’s Razor (or to stick with the popular Latin phrasings here, lex parsimoniae) in the very least can be used to show that the presumption of exclusion of these properties is the less defendable position.