Jaegwon Kim once told me that he thought secondary qualities were intrinsic if anything is. Since that time, he seems to have shifted from being a reluctant defender of reductionist functionalism to a reluctant adherent of something like Chalmers' view (a relatively small shift, since in each case the reluctance consisted of his strong pull toward the other of the two options). As I've alluded to in the past here, and here, I think the view that qualia are intrinsic is important to the debate about qualia.
I shall approach this topic from a distance; at the most abstract level of fundamental metaphysics, it seems to me that staying away from intrinsicness has produced some spectacular results. Buddhism teaches that there is no self with any intrinsic nature; the self is just a placeholder in a network of relations. To put it somewhat tendentiously (as the Buddhists themselves sometimes did), the self is an illusion. This view did not, of course, maintain that the self was an illusion in the midst of a world of non-illusionary things; the world experienced by the self is also an illusion on this view. There's just a network of relations, with things being only placeholders for positions in the network.
I suspect that this is why it was Indian mathematicians who invented the concept of zero; to the ancient European mathematicians, numbers were things, and so an absence couldn't be a number. This is also why the Pythagoreans got so stressed out by irrational numbers; they could make sense of a ratio between countable collections of things, but how could something that wasn't either a count of things or even a ratio between such counts exist? To the Indians, on the other hand, numbers as placeholders in a network of relations no doubt seemed natural (since they were used to thinking in that way anyway), and it's obvious that idenfying the zero spot in the network of relations is useful. This view of mathematics as being about such relations is of course orthodoxy in modern times, and has been very good for mathematics.
I think it's not just good for mathematics. Intrinsic properties just cause trouble; structures and relations are where all of the answers are to be found. I think we shouldn't believe in intrinsic properties anywhere. This is somewhat of a paradoxical position, admittedly, and of course there are some, such as Rae Langton, and if her plausible account is right, Kant, who think that while we can't know anything intrinsic, there must nonetheless be intrinsic properties. I find such views even more puzzling than a complete rejection of intrinsic properties; we can know there are these specific things we can't know about? But Kant scholars have been debating that sort of thing endlessly since his own time. I shall leave it aside for now, as the topic I'm most interested in involves qualia, and qualia are not supposed to be uknowable. So take just the place where extremists like myself agree with Langton and Kant and other moderates; we can't know anything intrinsic.
This is enormously relevant to the issue of qualia. Phenomenal character appears to be an intrinsic property of experiences. This, it seems to me, is the main intuitive obstacle to a functionalist account of phenomenal qualities: functional properties are quite obviously non-intrinsic. But if the intrinsic can't be known, then apparent intrinsicality is always an illusion. And if such appearances are always misleading, then they're misleading in this case, so the intuitive obstacle can be swiftly dismissed.
This also strikes me as being the real heart of a lot of the arguments surrounding anti-materialist theories of qualia. Lewis, for example, in "What Experience Teaches," goes through a very lengthy discussion of what knowledge of phenomenal qualities can't be like. It seems to me that a good short summary of the argument is that if phenomenal qualities are to serve the role they are supposed to serve in Jackson's knowledge argument, they must be intrinsic, but looking at all of the things we know about our experience, it turns out that we can't find any role for anything intrinsic; looking for knowledge always turns up extrinsic things.
To take another example, it seems to me that Chalmers' zombie argument works by asking us to separate out the intrinsic properties of experience, and imagine that they're absent in the zombie world. Obviously, if experience has no intrinsic properties, this procedure is impossible; either all worlds are zombie worlds, or (more reasonably) there's some account of phenomenal experience in terms of relational properties, and any world with the right relational properties has phenomal experiences.