I think there is a version of naturalism that seems to explain the relevant range of data better than theism. To be a tad more precise: there is a prima facie viable version of naturalism that (a) explains the data appealed to in theistic arguments at least as well as theism, and (b) there is a range of other data that is better explained by this version of naturalism than by theism. Below I will provide a brief sketch of the sort of view I have in mind, as well as some considerations in its favor vis-a-vis theism.
Thus, consider the following hypothesis, which I'll call 'Chalmersian Liberal Naturalism' (in honor of the contemporary philosopher David Chalmers, who appears to accept a view somewhat similar to it. Call the view 'CLN' for short):
(CLN) There are both abstract objects and concrete objects. The abstract objects are eternal, necessary beings. All concrete objects are composed of just one kind of substance, and its essence has both physical and phenomenal or proto-phenomenal (or at least representational or proto-representational) attributes as a part of its essence (alternatively, the one kind of substance is neither physical nor mental, but the physical and mental are composed of it). Furthermore, this kind of substance is factually or metaphysically necessary. It is also eternal, and comprises a multiverse.
It seems to me that CLN can explain all the data appealed to by the standard arguments of natural theology: we'd expect fine-tuning if for every possible combination of fundamental constants, there is a universe that instantiates it -- indeed, a finely-tuned universe is inevitable on such a hypothesis; we'd expect consciousness in animals and humans if proto-phenomenal states are a part of the essence of concrete substance, since consciousness logically supervenes on structures composed of such a substance when it is suitably complex, and such complexity is accounted for in terms of mutation and natural selection; we'd expect abstract objects if they were eternal, necessary beings; we'd expect moral properties if they logically supervene on certain states of affairs, the latter of which are abstract, necessary beings that contingently obtain or fail to obtain; and the contingency of objects in the world is explained in terms of the factually or metaphysically necessary stuff of which it's composed.
Furthermore, it seems to me that CLN explains a wide range of other data better than the hypothesis of theism. Thus, if CLN were true, then we'd expect the data of huge amounts of prima facie gratuitous human and animal suffering; we'd expect the data of divine hiddenness; we'd expect the data of radical religious diversity; we'd expect the data of scientific studies involving double-blind experiments indicating the ineffectivenss of prayer; and we'd expect the religious demographics data that we actually have. However, we wouldn't expect such data if theism were true.
Thus, it seems to me that CLN explains not only all the data appealed to in theistic arguments at least as well as theism, but it also better explains a wide range of data that is only awkwardly explained if explained at all by the hypothesis of theism. But CLN is a version of naturalism. Therefore, I conclude that naturalism is a better explanation of the range of relevant data than theism.
Some objections and replies:
Objection 1: "CLN is too weird to be true!"
Reply: True, CLN is weird. However, I don't know how to validly argue from "x is weird" to "x is false". A theory accrues support in virtue of embodying various theoretical virtues (simplicity, explantory scope, explanatory power, etc.), and so the theory stands or falls on that basis and that basis alone. Furthermore, CLN is certainly no weirder than the hypothesis of theism. For compare CLN to theism:
T: The world is composed of two really distinct kinds of substance: purely physical substances and purely immaterial substances. Furthermore, these two sorts of substances are capable of interacting with one another. In addition, there are both finite and infinite immaterial substances -- human (and perhaps animal) souls and God -- and the infinite immaterial substance created the finite immaterial substances (and perhaps the material ones, too), and created them without pre-existing materials (i.e., out of nothing).
Things get even more exotic if we move to specifically Christian theism, with its additional doctrines of the trinity and the incarnation. But the point is that both hypotheses -- theism and CLN -- include odd and problematic theses, and when one does a "cost-benefit analysis" of the two views, comparing the oddities and problematic features of the two hypotheses, it seems to me to be, at best, a wash.
In any case, it's a mistake to think that one must be a Liberal Naturalist to accept the conclusions here. One could be a Conservative or Moderate Naturalist -- or even a skeptic or agnostic -- and yet still properly accept the crucial claim here, viz., that whether it's the actual explanation of the relevant data or not, it's a better explanation of the data than theism -- or at the very least: as good an explanation of the data as theism --, in which case the data doesn't favor theism over naturalism.
Objection 2: CLN is too complex to be plausible.
Reply: Two points. First, CLN posits two sorts of entities -- abstract and concrete -- and they require separate treatment. As to the former: Since the abstract objects are posited as necessary beings, they need no explanation. That leaves us with the realm of concrete objects, and here we have postulated one type of substance, which in turn gives rise to a multiverse. Is this hypothesis complex?
Well, it's complex in one sense; in another it's not. The objector mistakenly assumes that there is only one kind of theoretical parsimony, viz., *quantitative* parsimony (i.e., the explanation postulates fewer entities). However, as David Lewis has taught us, another type is *qualitative* parsimony (i.e.,the explanation postulates fewer *kinds* of entities). And while the theistic hypothesis is a much more *quantitatively* parsimonious explanation of the data (it explains all of the data in terms of just one entity, viz., a god), the CLN multiverse hypothesis is a more *qualitatively* parsimonious explanation of the data (since it explains all of the data solely in terms of one *kind* of entity, viz., Chalmersian panprotopsychist substance). And it's not clear which type of theoretical parsimony is more important here.
 Objection: "but I can imagine the fundamental stuff failing to exist. And since conceivability is sufficient evidence for possibility, it's possible for the fundamental stuff posited by CLN to fail to exist, in which case we have reason to doubt that such stuff is metaphysically necessary, in which case it can't explain the data of contingency." Reply: Either conceivability is sufficient evidence of possibility or it isn't. If it isn't, then of course the data of the conceivable non-existence of a Chalmersian multiverse isn't sufficient evidence of its possible non-existence, in which case the objection fails. On the other hand, suppose conceivability is sufficient evidence of possibility. Then since it's conceivable that both God and the Chalmersian multiverse fail to exist, then there's sufficient evidence that it's possble that both God and the Chalmersian multiverse fail to exist, in which case it looks as though no being of the relevant sort could be metaphysically necessary, in which case the jig is up for arguments from contingency, in which case contingency falls out of the range of data that needs explaining. Either way, then, the objection fails.