So, a better intuitive basis for rejecting naturalism, it seems to me, is that it can't accommodate the datum that debates about the distribution of mental or moral properties are substantive. Imagine two people disagreeing about precisely which collection of atoms constitutes the Sun. (There's overwhelming overlap between the two proposals, they just differ slightly in where they draw the boundaries -- whether or not to include a particular borderline atom, say.) It's clear that this is a merely terminological disagreement: they diverge in whether they take the word 'Sun' to pick out the minimal collection S, or the one-atom-larger collection S*, but it's not as though there's some further issue at stake here about which they remain ignorant -- which collection of atoms has some putative special further property of really being the Sun. There is no such further property.
Disagreements about the distribution of minds and moral properties are not like this. But if naturalists were right, they should be. As I wrote in an old post on 'non-physical questions':
The question whether my cyborg twin is conscious or not is surely a substantive question: I'm picking out a distinctive mental property, and asking whether he has it. Now, the problem for physicalists is that they can't really make sense of this. They can ask the semantic question whether the word 'consciousness' picks out functional property P1 or biological property P2. But given that we already know all the physical properties of my cyborg twin (say he has P1 but not P2), there's no substantive matter of fact left open for us to wonder about if physicalism is true. It becomes mere semantics.
In other words, in order for it to be a substantive fact that consciousness tracks (say) functional rather than biological properties, there needs to be a further property (distinct from the functional and biological properties) for the two views to both be arguing about. Otherwise they're just arguing about a word. But it's obvious that disputes about the boundaries of consciousness are not just disputes about the word (in stark contrast to disputes about the boundaries of the Sun).
Similarly in metaethics:
The whole problem for the naturalist is that they have no basis for claiming that any particular one of the competing, internally coherent moral theories is the one true moral theory. After all, given the natural (non-moral) parity between us and our Moral Twin Earth counterparts, what in the two worlds can the naturalist appeal to as the basis for a moral or rational asymmetry between us?
If moral boundaries are not just to be determined by arbitrary semantics, it must be that there's a metaphysical difference between the truly good properties and the pretenders, breaking the symmetry. There must be a further property of goodness for the rival views to be arguing about.
I think this is the core intuition that's really behind the Open Question Argument, Parfit's triviality and fact-stating objections, as well as the knowledge argument in philosophy of mind. But I'm not sure if anyone has put the point in quite this way before?