I think it is important to distinguish the supernatural from the miraculous especially inasmuch as their conflation aids and abets the 'Dawkins Gang.' (That's my mocking moniker for Dawkins, Dennett, Harris, Hitchens, and their fellow travellers.) Let's briefly revisit Daniel Dennett's definition of religions as
. . . social systems whose participants avow belief in a supernatural agent or agents whose approval is to be sought. This is, of course, a circuitous way of articulating the idea that a religion without God or gods is like a vertebrate without a backbone.(Breaking the Spell, p. 9, emphasis added)
But what is meant by the crucial term 'supernatural'? The natural, for Dennett, is that which obeys the laws of nature, the laws of physics and biology for instance. (p. 25) The supernatural, therefore, is that which violates these laws. The supernatural is thus the miraculous. (p. 25) So when Dennett says that the participants in a religion avow belief in a supernatural agent, he implies that they avow belief in an agent whose existence and mode of action are miraculous, i.e., in violation of the laws of nature.
But this identification of the supernatural with the miraculous is seriously problematic. For it is obvious that one who affirms the existence of God need not be affirming the existence of something that violates natural laws. The laws of nature govern the material world. (Or, if you insist, they describe or codify the regularities of the material world.) But God is not a member of the material world, or identical to the material world. (Pantheism is not on the table.) So the laws of nature do not apply to God. But it does not follow that his existence violates these laws unless it is also a law of nature that only material (physical) beings can exist.
Could it be a law of nature that only material beings exist? Equivalently, could it be a law of nature that only nature exists? I say no, but to save keystrokes I won't argue for this (obvious) thesis now. But we should note that if Dennett or anyone thinks that it is a law of nature that only nature (the space-time-matter system) exists, then Dennett's definition rules out the possibility of a supernatural agent. It is surely self-evident that any adequate definition of religion that stipulates that religious believers posit supernatural agents must leave it open whether or not there are any supernatural agents. Otherwise, Dennett's definition of religion would boil down to this:
A social system whose participants avow belief in a supernatural agent, i.e, an agent whose existence violates natural laws, the only laws there are.
That would be like defining a theist as one who affirms the existence of a nonexistent being (having certain omni-attributes) and an atheist as one who affirms the nonexistence of a nonexistent being (having certain omni-attributes). But surely the belief the theist avows is a belief that the omni-qualified being exists. If the theist's belief were of a being that was believed to be nonexistent, then the theist wrould be involved in a sort of performative inconsistency, just as the atheist would be involved in a sort of performative tautology were his belief to be characterized as a belief that a nonexistent omni-qualified being does not exist.
To put it another way, if you want define religion in terms of the beliefs of certain people, then you must characterize those beliefs from the point of view of the believer, and not from a point of view external to the believer.
To say of X that a certain set of laws does not apply to it is not to say that X is in violation of those laws. The laws of planetary motion do not apply to abstract object (numbers, Fregean propositions, etc.) but these objects do not violate these laws. On the other hand, the laws of logic do not apply to physical objects — except insofar as they are described, conceptualized or made the logical subjects of propositions — but this is not to say that physical objects violate the laws of logic.
To cite another example, the gas laws do not apply to intentional states such as desiring and hoping, but that is not to say that the latter are in violation of the gas laws. Do my thoughts expand in the summer time? They neither expand nor fail to expand: they do not belong to the category of entities for which expansion or the opposite is an 'option.' But that is not to say that my thoughts violate the laws pertaining to expansion and contraction.
Therefore, it is a mistake to say or imply that the existence of a divine agent is supernatural in the sense of being miraculous (natural law violative). Indeed, the divine transcendence insures that God cannot be miraculous in this sense. In plain English, God is not in nature so he cannot violate any law of nature.
It follows that a participant in a religion need not affirm the existence of a supernatural agent in Dennett's sense of 'supernatural.' Dennett's definition is inadequate.
There are two senses of 'supernatural' that we need to distinguish, and that Dennett may be conflating. In Dennett's sense, the supernatural is the miraculous, where the miraculous is that which is in violation of physical laws. In the second sense, the supernatural is simply that which is not part of nature, the system of space-time-matter.
God is a supernatural existent in the second sense but not in the first. How can the existence of God violate any law of nature if God is not in nature? There is nothing miraculous about the very existence of God. No doubt God is meta-physical and super-natural; but that is not to say that God's existence is miraculous.
Now let's briefly consider the question whether the action of God must violate natural laws. Although there is nothing miraculous about the existence of God, it is a further question whether the action of God is miraculous. I want to say first that God can act on nature without intervening in nature. He could sustain it in being without interfering with any of the causal chains that occur in nature. So it is false that God's action must involve the violation of natural laws.
It seems, therefore, that one could be a theist while maintaining that God is wholly nonmiraculous both in his existence and in his action. I do admit, though, that this theism is a bit of an abstraction from the theism of the Abrahamic religions. In these religions, God is represented as intervening in nature's workings. His relation to nature is not merely a 'vertical' one of ontological sustenance, but also from time to time a 'horizontal' one whereby he interferes with causal chains within nature. In the Abrahamic religions God does not merely act upon nature, he acts within nature. If a miracle is defined as a violation or suspension of a natural law, then God's acting within nature is miraculous.
Whether or not miracles are possible, my point is that neither the existence of God nor God's acting upon nature are miraculous. The confusion of the supernatural and the miraculous must be avoided.
I conclude by noting that there is something deeply problematic about Dennett's definition. He defines religion in terms of the avowal of belief in supernatural agents. But it turns out that a supernatural agent is one whose existence and mode of action is miraculous, i.e., in violation of natural laws. But surely no sophisticated religionist — no religionist worth refuting in a 450 page book — thinks that God's existence violates natural laws. The only way the existence of God could violate natural laws would be if God were a part of nature; but that is not what sophisticated theists believe. Dennett's definition is inadequate because it attributes to the religionist beliefs he does not hold. (It is also inadequate because of the conflation of religion with theism, but that is a secondary matter.)
The problem may be due to an equivocation on 'supernatural' as between violative of natural laws and transcendent of the system of space-time-matter.