Here is an old argument of mine that Hume's Dialogues Concerning Natural Religion should, despite the title, be read more as a work in the philosophy of science than in the philosophy of religion. It lacks one of the things it needs, namely, a discussion of the weaknesses of taking the Dialogues chiefly as a work in philosophy of religion (there are several). But I still think, by and large, it's on the right track.
In essence, all the following arguments are based on recognizing that the primary topic of the Dialogues is the intelligibility of the world. In particular, it looks at this position, The order of the world is analogous to rational design, and determines how far and to what degree it can be held.
I. External reasons
A. Historical: Given the historical context of the Dialogues, reading them as a work of philosophy of science makes good sense. My argument is this:
The Dialogues are on the subject of natural religion.
One of the types of questions that were understood to fall within the field of natural religion at the time was the question of the ultimate foundations of the scientific enterprise. One finds this in (just to name a few):
Robert Boyle (on final causes)
Isaac Newton (in the Optics)
Richard Bentley (in his Boyle Lectures against atheism)
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).
Therefore it is reasonable to view the natural religion of the Dialogues as a ground on which questions about the ultimate foundations of the scientific enterprise are asked and certain answers to these questions (e.g., the design considerations of all four thinkers above) examined.
B. (More) Contemporary: The Dialogues discuss a subject which have been shown since its time to be of interest to those interested in the basic foundations of the entire scientific enterprise, and therefore reading them as philosophy of science can contribute to a perennial philosophical interest.
Some examples of people who, in looking at scientific work, have been interested in the topics covered by the Dialogue are:
Paley, Herschel & Whewell. British natural religion in the 19th century has obviously connections with the topics of the Dialogues. Note in particular that Herschel and Whewell are the 19th century's greatest philosophers of science; and that their design considerations are in many ways closely related to their work in the philosophy and history of science.
Kant. His work both on the conditions of the possibility of science and on the design argument necessarily bring him to topics discussed in the Dialogues.
Darwin, Huxley, et al. A number of issues touched on by the Dialogues have been essential to determining the status--and proper procedure--of biology. This goes back to Harvey and Boyle, although not exclusively to them, and is derived especially through Paley, whose texts were standard biological fare for a good portion of the 19th century. Darwin in part built his theory in conscious opposition to Paley (it has recently been recognized in a number of works on Darwin how heavily he was influenced, both positively and negatively, by Paley, and how significant the problem of animal suffering played in his thought). Huxley (in part) draws directly from the Dialogues, and he influences, in various ways, much of the 20th century.
Planck & Einstein. The scientific realism of both of these is related to thoughts pertaining to the topic of the Dialogue (in both cases generally influence by Kant). Einstein has some of the pithiest sayings along these lines, but the best formulation is probably in Planck's Scientific Autobiography.
Therefore discussing the Dialogues as philosophy of science can potentially contribute even to contemporary discussions, since its topics have a bearing on issues that have been discussed since Hume's time.
C. Scholarly: Let's level a moment. While there are exceptions, most scholarly work on the Dialogues has been, to be quite honest, mediocre at best. We find that treating the Dialogues as 'philosophy of religion' has led to preciously little fruitful research, little growth in our understanding of Hume, and interminable disputes about the same topics (e.g., Philo's 'change of mind' in Part XII, etc.). At the very least, a change of perspective should provide a breath of fresh air. Even if we are wrong, we will have learned something new. But I think we will find that reading the Dialogues as philosophy of science allows us to see and explore things in the Dialogues that have been simply overlooked. Further, it enables us to ignore those silly people who think that the Dialogues are the Absolute Apologetics of Atheism, conclusively refuting all theistic arguments, and to treat it in a more realistic fashion as a philosophical work treating of issues of interest to 'philosophy of religion' for a very limited, but still vital and important, purpose.
II. Internal Reasons
A. From Hume's Corpus Generally: 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. I argue thus:
The justification given by Pamphilus in the Preface to the Dialogues is based on natural religion's capacity to satisfy curiosity.
Hume 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 Dialogue 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.
Therefore it is reasonable to read the Dialogues as philosophy of science.
B. From the Dialogues Particularly: There are a number of evidences internal to the Dialogues themselves that Hume regarded them as discussing matters of importance to scientific inquiry.
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." This issue is explored by much of the Dialogues. See Beryl Logan's article, "Science and Skepticism" in Hume Studies.
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.
In Part III Cleanthes continues the discussion of scientific reasoning & confounds Philo.
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, but 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.
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.
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?
Therefore we seem to have good reason to focus at least as much, and perhaps more, on the philosophy of science issues, than on the philosophy of religion issues.