Dualism comes in a variety of forms. Examples include property dualism (Searle, though he denies it) and panpsychism (Chalmers, it seems). Regardless of the version expounded, all such dualisms divorce the mental from the physical, hence the dead horses that are the so-called mind-body problem or the problem of qualia. On this view of matter, we can't account for things like color because, by definition, matter does not have color in the way that we commonly understand it as having color. Physical theories, instead of explaining color, redefine color in other terms. The only place left to locate color, as it is commonly understood, is the mind that's been so brutally split off from matter. Fun fact: Cartesian dualism is not a "religious residue". It is a philosophical position. In its lingering incarnation, we can credit Descartes through whose work it bears an interesting relation to the development of modern empirical science. Prior to Cartesianism, Aristotelian views were dominant. Indeed, while the Roman Catholic Church does not have an "official" metaphysical doctrine (metaphysics is philosophical, not theological or doctrinal), the preferred metaphysical theoretical apparatus has been Aristotelian since Aquinas. No such dualism exists in Aristotle or Aquinas.
On the other hand, eliminativism manages to take an even whackier view of things than dualism. Whereas dualism has painted itself into a corner by refusing to reexamine its suppositions, eliminativism "resolves" the problem by shutting its eyes, that is, by denying the existence of those things it must explain. As a result, it is an incoherent position.
What's interesting is that Dennett does distinguish between "function" and "intention", though I'm not entirely sure how he reconciles (if he does at all) all of these with materialism. The reason I draw attention to this point is that teleology/final causality is frequently misunderstood owing to a confusion between conscious intent and function. When an Aristotelian talks about the "purpose" of an organ, he has in mind what the organ is ordered and organized toward, not what intelligent design theorists would describe as "design". (Interestingly, ID theories are also rooted in Cartesian ideas about matter and thus need to appeal to imposed, extrinsic divine intent to locate and explain the function of things like organs. Their scientistic (not scientific) opponents take the eliminativist approach and deny that organs have functions at all because they hold to the same concept of matter as ID theories while rejecting that divine intent exists. On the other hand, Aristotelianism maintains the intrinsic finality of things like organs and thus does not need to appeal to some externally imposed divine intent to explain function as such.)