The term ‘naturalism’ has no very precise meaning in contemporary philosophy. Its current usage derives from debates in America in the first half of the last century. The self-proclaimed ‘naturalists’ from that period included John Dewey, Ernest Nagel, Sidney Hook and Roy Wood Sellars. These philosophers aimed to ally philosophy more closely with science. They urged that reality is exhausted by nature, containing nothing ‘supernatural’, and that the scientific method should be used to investigate all areas of reality, including the ‘human spirit’ (Krikorian 1944, Kim 2003).
So understood, ‘naturalism’ is not a particularly informative term as applied to contemporary philosophers. The great majority of contemporary philosophers would happily accept naturalism as just characterized—that is, they would both reject ‘supernatural’ entities, and allow that science is a possible route (if not necessarily the only one) to important truths about the ‘human spirit’.
Even so, this entry will not aim to pin down any more informative definition of ‘naturalism’. It would be fruitless to try to adjudicate some official way of understanding the term. Different contemporary philosophers interpret ‘naturalism’ differently. This disagreement about usage is no accident. For better or worse, ‘naturalism’ is widely viewed as a positive term in philosophical circles—few active philosophers nowadays are happy to announce themselves as ‘non-naturalists’. This inevitably leads to a divergence in understanding the requirements of ‘naturalism’. Those philosophers with relatively weak naturalist commitments are inclined to understand ‘naturalism’ in a unrestrictive way, in order not to disqualify themselves as ‘naturalists’, while those who uphold stronger naturalist doctrines are happy to set the bar for ‘naturalism’ higher.
Let's take stock.
* "Naturalism", according to the SEP, doesn't even have a set definition. It apparently adds up to "rejecting the supernatural" and "liking science". Of course, what's supernatural if "natural" isn't really defined? One would think the "liking science" part would be easier, but then there's that damn Demarcation Problem. One would be tempted to say "Well, naturalism is physicalism!", but then you go to the SEP entry for physicalism and see nearly equivalent problems with defining "physical".
* But many philosophers (And, I suppose, scientists and wannabe philosophers/scientists) want to be called naturalists anyway. The SEP implies that this results in some self-declared naturalists believing in things that other ("Stronger"?) naturalists would call supernatural. But that's alright, because the SEP says it would be fruitless to try and find an "official way" of understanding naturalism.
* The innate humor of self-described naturalists insisting that science can explain all of creation, while they have tremendous difficulty *defining what naturalism even is*, is tremendous.
* It goes without saying that if a solid definition of naturalism is hard to come by, a solid definition of supernaturalism is just as or even more hard to come by. Again, there's some innate humor here.
* It's hard to ignore the whiff of social and political positioning indicated by this stated desire to be called a "naturalist", even while the term itself has a fairly elastic (vacuous? arbitrary?) meaning. That the SEP should admit that there is a strong urge to call something "naturalistic" because the general feel or attitude towards the term is positive, should raise up serious warning flags.
I get the impression that "naturalist" philosophers would make for interesting objects of study for sociologists and anthropologists. Even psychologists.
My response to all of this is to just say, to hell with it - I'm a naturalist. So's Thomas Aquinas. Orthodox and traditional catholicism are just a form of naturalism. Dualists are naturalists. Panpsychists are naturalists. Voodoo practitioners and cargo cultists have a flawed naturalistic belief, little different from believing in a phlogiston.
And the funny thing is, as near as I can tell, few philosophers are able to say I'm wrong about this. The best they can do is take a vote, or report to me what their feelings are. But they can't refer to any definition of naturalism I'm in violation of, because all indications are that the term is shockingly empty. It's little more than a flag to rally around, a symbol. And it's easy to co-opt a symbol.
So in the immortal words of Emperor Zombie: Mine now.