I brought it up in comments, but it seems worth highlighting: Hegel’s Lectures on the Philosophy of Religion, arguably the founding documents for philosophy of religion as a specific subdiscipline, represent a much more capacious kind of reflection than that found in contemporary analytic philosophy of religion. Despite its obvious flaws, it does make an effort to reflect on the nature, role, and origin of religion and does so through a systematic reflection on as many religions as possible, as opposed to the contemporary focus on monotheism and proofs of God’s existence. For all that, it also seems to be clearly different from mere “sociology of religion” (something that the relatively new commenter Jim H. brought up but that has come up multiple times before in similar discussions), whatever “sociology” might be.
Kant’s Religion Within the Limits of Reason Alone is another example of philosophy of religion rather than what I’ve called “philosophy of God” or “philosophical theology.” As he must be in the wake of Critique of Pure Reason, Kant is strictly agnostic about whether God really exists and instead assesses religious ideas and institutions — including finding perhaps unexpected potential therein. He is not struggling over the existence of God, but over the place of religion in society. Indeed, he is clearly advocating for actual existing religious institutions that in some ways approximate his ideal of a “religion of pure reason” (i.e., Christian churches, which are at least in theory open to all comers and purely voluntary associations) should move further in that direction. Mendelssohn’s Jerusalem has similar goals, and Schleiermacher’s On Religion: Speeches to Its Cultured Despisers is much more concerned with defining religion as a distinctive area of human experience than with arguing for God’s existence. (Coincidentally, the first half of my course is structured around these three texts.)
In fact, I would even claim that the “new atheist” books contain a significant amount of philosophy of religion, albeit of a kind that I find to be overly simplistic — even if they do spend a lot of time on proofs of the existence of God and other religious beliefs they think are false, the overall impetus of their work is convincing others that religion (the human practice) is bad and should be abolished.
What distinguishes philosophy of religion from something like “sociology of religion” is a more-than-descriptive element — a theoretical or evaluative purpose that goes beyond a “just the facts” standpoint. There will be overlap between philosophy of religion and social-scientific approaches, just as there is an overlap between (what I’m calling) philosophical theology (but is most often called philosophy of religion) and doctrinal theology, but the distinctiveness of a philosophical or theoretical approach remains. To point out a minor example that nonetheless makes a big difference, a social-scientific study of Christianity would tend toward nominalism insofar as its bias would be to define Christianity (or whatever religious tradition) as “anything claiming to be Christian,” with as little judgment as possible. A philosopher of religion would be much more willing to take a stance on what Christianity (or whatever particular religious tradition they’re investigating) is and would be willing to come up with non-extrinsic evaluative standards for various examples of that religion.
More importantly from my perspective, the philosopher of religion would be particularly attuned to the unexpected resources that religion offers to thought. Straightforward examples here would be the reinterpretation of religious texts or the analysis of religious concepts. “God” might be included among those concepts, but it would not necessarily be the most important or fruitful concept.
The question here then becomes what separates philosophy of religion in this sense from theology, which I define as critical reflection on a particular religious tradition. I’d propose the difference is one of degree rather than kind, where one’s relative status (or assumed scholarly persona) as an insider or outsider would place one further on the scale toward theology or philosophy of religion, respectively. Someone like Altizer would be toward the outer edge of theology, while Marion might be closer to the outer edge of philosophy of religion — perhaps not perfect examples, but I hope a decent starting point.
In short, I believe that the philosophical tradition already includes significant examples of work that is not strictly the assessment of the truth-value of religious claims (which philosophy of religion in practice seems to be mostly limited to today), but is also not a purely descriptive social-scientific approach to religion. Insofar as I am a philosopher of religion, I would locate myself within that strand of the tradition, rather than the strand that currently monopolizes the actual existing subdiscipline of philosophy of religion, and I believe most of my compatriots here would do the same.