> Why not both?
Because those are mutually exclusive options. Either something is ontologically fundamental, or it's not. It can't be both.
The problem is probably the definition of "real".
I'm not arguing that consciousness is a fundamental property of the universe when I say it is real. The jury is still out but that's not what interests me the most. When I say "real" I'm talking about my subjective experience. It is real in the sense that it is something that I know I experience, regardless of the mechanisms involved.
Ultimately, what I'm interested in is finding out how it arises. Explaining it. Reducing it to its "third-party objective facts" if possible. Being able to look at a machine that mimics us and tell if that machine is experiencing something comparable to what we experience.
"is the qualitative experience of consciousness actually real, or is it reducible to third-party objective facts"
Why not both?
The "real" refers to our subjective experience. That there is something that is like to be me. Something that is like to be a bat. And at least under certain definitions, that's what we call conscience. That something I know I experience and that I doubt a computer is experiencing too.
Why would this be incompatible with reducing this experience to third party objective facts? We simply don't know but I don't see why we couldn't.