When I hear theists raise questions about what is natural, I often get the feeling that they are deliberately blurring the line between natural and supernatural so as to cast doubts on the naturalists' way of thinking about what exists and what doesn't. By trying to make it seem as if there is no reasonable definition for "natural", they then believe they are justified in denying the naturalist's claims that supernatural things don't exist, or at least to make the case that there is no definitive way to distinguish one from the other.
In blurring the line, they can can try to make naturalism too restrictive, so that it doesn't include various observable phenomena that they would like to claim as belonging to the realm of the supernatural. They may, for example, use a definition for "natural" that is equivalent "physical", and then proceed to define that as something that has spatial extent. This leaves the door open for noting the existence of various things have no spatial extent, and denying that they are natural. Mental phenomena are examples of this. The obvious problem here is that physical things include more than just material objects. They also include things like forces, potential fields, processes and behaviors. And in the view of many naturalists, mental phenomena are physical processes of the brain.
By having a more extensive view of what is physical, we are able to encompass everything that is objectively observable in the realm of natural physical reality. But this still leaves theists with some room to keep the line on the restrictive side. We (mostly) all agree that mental phenomena exist, but they are not objectively observable. Naturalists claim that they are natural, and theists claim that they aren't. The theists' argument is based on the idea that there are aspects of mental phenomena, like intentionality, that can't in principle be explained by natural means. "How can a thought in the brain be about something outside the brain?" they ask. Of course, they are wrong about that. Everything we think about is represented in the brain, and concepts in the brain have physical connections between them The fact is that theists simply refuse to accept any natural explanations, preferring instead to cling to the age-old refrain: God did it.
Another approach they take, often in the same discussion, is to blur the line in the other direction - to make naturalism so inclusive that it encompasses all phenomena, including any potential supernatural events, and thus it has no meaning. If the naturalists says that everything that exists is natural, then any event that is unexplained by science would have to be considered to be natural. This would include things described in the biblical accounts of resurrections, walking on water, etc. The rationale of the theist here is based on eliminating science as the arbiter of what is natural and what isn't. If science can't explain something today, that doesn't mean that it won't be able to at some time in the future. Therefore, science is in no position to claim that these biblical events aren't natural, or that they can't happen. And that implies that the naturalist has no leg to stand on.
In this case, the theist is denying what is at the very core of science and naturalism. It is the observation that things behave in patterns of regularity. The goal of science is to discern and describe these patterns, which we call laws of nature. It is true that there may still be undiscovered patterns of behavior for things that have yet to be observed, but that doesn't imply that anything is possible. A rock doesn't float up into the sky without some external force acting on it, and water doesn't spontaneously turn into wine. We know this because we have observed the regular behavioral patterns of these things. While there may still be unknown physical laws, any such law would still necessarily involve regularities of behavior - not one-time violations of the regularity that has always been observed. So it is still unreasonable to think that water may change to wine due to some as yet unknown law of nature. This is a crucial distinction that many theists just don't seem to understand.
Yet another way for theists to blur the line between natural and supernatural is to place them both on the same epistemological level. They describe naturalism as being founded on circular reasoning. This is based on the idea that naturalists supposedly think science is the only legitimate source of knowledge, but science depends on scientific methods to validate its beliefs. Therefore, there is no legitimate foundational basis for scientific or naturalistic beliefs. When it is pointed out to theists that their belief in supernatural entities is no less circular than that, the honest ones will admit as much.
The naturalist may complain that I have been drawing my picture of the reality with which RE [religious experience] allegedly puts us in touch from RE itself, and this is circular. But there is no escape from that kind of circularity. We are in the same situation with respect to SP [scientific procedure]. - William Alston - What is Naturalism, that We Should Be Mindful of It? (pg 14)Any reasonable epistemologist understands that beliefs are warranted if they are justified by being derived from properly basic knowledge, and that theism has no such basis (unless you buy Planinga's thesis that subjective religious experience is properly basic knowledge). But the same is not true of scientific knowledge, which is empirically based. Epistemology has always held that sensory information constitutes properly basic knowledge. And what is observed by the senses is the foundation of scientific knowledge. Therefore, it is not correct to say that scientific reasoning is inherently circular. Unlike religion, science has the advantage of being based on objectively observable facts.
I propose a way of defining "natural" that would help to limit theists' ability to blur the distinction between the concepts of natural and supernatural: Something is natural if it is caused by, and it behaves in accordance with the observable regular patterns of natural law. I don't think this is a circular definition. If you don't like the term "natural law", think of it as just regularity of behavior that is observable, at least in principle. This definition excludes events like water changing into wine, which violates regular behavioral patterns, and it excludes spirit-beings like God, which have no cause in natural law. It may leave open the question of mental phenomena for theists who doubt their natural causation, but that opening is getting tinier by the day.
At any rate, if theists want to use vague and unrealistic definitions of naturalism to make naturalists sound unreasonable, it is only appropriate that a better definition be placed on the table. This definition may not be perfect, but it leaves less room for theists to equivocate and muddy the water on what is natural.