Extreme naturalism or consistent naturalism?

Paul Draper wrote: "Extreme naturalism" is the conjunction of naturalism with the thesis that

X: Either (i) beliefs don't exist (eliminativism) or (ii) they exist but they don't affect behavior at all (epiphenomenalism) or (iii) they exist and they affect behavior but not by virtue of their content (semantic epiphenomenalism) or (iv) they exist and they affect behavior by virtue of their content, but to have a certain content just is to display a certain set of third-person properties (reductive materialism).

Now is this extreme naturalism, as Draper seems to think, or is this just consistent naturalism, as I think. I think that the causal closure of the physical leads to this conclusion, while the denial of the causal closure of the physical results in an inconsistent naturalism.

Draper adds: Sensible naturalism is just naturalism conjoined with the denial of X. In other words, it conjoins naturalism with

S: Beliefs exist, they affect behavior by virtue of their contents, and a belief's having a particular content is not the same as its displaying a certain set of third-person properties.

In which case the physical isn't causally closed, and from the point of view of the physical, miracles are occurring. It looks tempting to go there given the difficulties for each of the other types of naturalism, but it isn't going to work. If all the naturalist is trying to do is avoid traditional theism, yeah maybe. If what you are trying to do is maintain a position consistent with the views traditionally ascribed to natuarlists, I don't think so.