Hume's Dialogues Concerning Natural Religion, I would suggest, are less about natural religion than about the foundations of science. Just a few indications that this is a fruitful way of looking at them:
* Given the historical context of the Dialogues reading them as a work of philosophy of science makes good sense. The Dialogues are on the subject of natural religion. One type of question that was understood to fall within the field of natural religion at the time was precisely the question of the ultimate foundation of the scientific enterprise, and various corollary subjects. Examples:
a. Robert Boyle (on final causes)
b. Isaac Newton (in the Optics)
c. Richard Bentley (in his Boyle Lectures against atheism)
d. Nicholas Malebranche (Search 2.1.4, LO 98-100)
Discussions of these issues have strong resonances with points found in the Dialogues: e.g., final causes, Newton's Rule 1 (on the use of simplicity in science: Nature does nothing in vain), some of the arguments of people like Bentley and Malebranche against the Epicurean hypothesis (which was understood to argue that all things come about by chance rather than by divine providence).
* Reading the Dialogues as philosophy of science fits well with some of what Hume says elsewhere. Most importantly, it explains why Hume considered natural religion to be a legitimate field of philosophical inquiry, for all that he dislikes its tendency to excess. The justification given by Pamphilus in the Preface to the Dialogues is based on natural religion's capacity to satisfy curiosity. Hume, however, always associates the motive of curiosity with valuable and legitimate (although not always perfect) inquiry: in science (History), in Hume's own philosophical work (Treatise 1.4.7), and elsewhere (Treatise 2.3.10). Therefore it is reasonable to think that Hume considers natural religion to have some genuine value. What could that be? One of the other works in which Hume discusses issues relevant to the Dialogues is The Natural History of Religion. There Hume associates design considerations with the rise of monotheism, with which he considers it to be associated. One of the fundamental notions of NHR is that of the 'frame of nature': what distinguishes true religion from superstition is that the former is based on 'enquiries into the frame of nature', consideration of natural laws, and is motivated by curiosity or love of truth (Sect. II). Now, NHR is an extremely difficult work to interpret, and there is no fully convincing interpretation of it available, in part because it is irony-laden: Hume says things he certainly doesn't mean, and other things that he might not mean. There is, however, some reason for taking seriously certain elements of what Hume says here--namely, that design considerations become a live issue when, motivated by curiosity, we make 'enquiries into the frame of nature.' NHR, after all, is not one long piece of irony; it has a serious purpose, namely, to describe the natural history of religion. Associating design-monotheism with curiosity and inquiry is essential to the success of Hume's account. Therefore, it does not seem reasonable to regard this characterization as ironic, especially since there is nothing here nor anywhere else in Hume to suggest that we should treat it as ironic. Therefore it is reasonable to place the value of natural religion in its involving 'enquiries into the frame of nature' motivated by curiosity. Reading the Dialogues in the way I have suggested would make them in reality concerned with 'enquiries into the frame of nature' motivated by curiosity.
* There are a number of evidences internal to the Dialogues themselves that Hume regarded them as discussing matters of importance to scientific inquiry.
1. Cleanthes in Part I links the fortunes of natural religion with the sort of inquiry done in Newton's Optics and the works of Copernicus and Galileo. Philo's skepticism, as Cleanthes sees it, "is fatal to knowledge, not to religion." That is, skepticism in religious matters cannot & should not be such as to involve skepticism in scientific matters. This issue is explored by much of the Dialogues. There's a useful paper on this point by Beryl Logan, called "Science and Skepticism" (in Hume Studies, I think).
2. The discussion of Part II is thick with examples of successful and failed scientific reasoning, and ends with Galileo and Copernicus again, this time discussed by Philo.
3. In Part III Cleanthes continues the discussion of scientific reasoning & confounds Philo.
4. Demea at the end of Part III shifts the discussion again to what the experimental inference tells us of the nature of God. This is the topic of discussion in Part IV, and here again Philo still discusses scientific reasoning, focusing on its limits. This continues to be the case as Philo presses his case over the next several parts.
5. In Part XII Philo takes the trouble to reconcile his approach with the simplicity considerations involved in the choice of (again) the Copernican system by people like Copernicus and Galileo, as well as with the Newton-approved maxim, Nature does nothing in vain.
6. Therefore there is reason to believe that a major concern of the Dialogues is the nature and limitations of scientific reasoning itself: How far can the experiment inference actually carry us?
In a sense, the Dialogues can be seen as asking the question: Do you have to be a theist in order to allow the world sufficient intelligibility for doing science? (I've discussed Hume's answer to this question elsewhere.)