I recently accepted to be an executive editor for the Journal of Analytic Theology, and will be joining the team with Mike Rea and Oliver Crisp (senior editors) and Kevin Diller (executive editor). JAT is an open-access, interdisciplinary journal that fosters analytic approaches to theological topics, including analytic philosophy of religion. I'm excited to be a part of this, and it will be my first major editorial role (I'm on the board of other journals but it's not quite the same as co-managing a journal).
One thing I've noticed among analytic philosophers of religion is that they are fairly orthodox. You don't see analytic philosophers of religion (hence aPoRs) defending, say, Arianism or Pelagianism. Indeed, you will often see aPoRs arguing at length something like "Now at first, my approach may seem Pelagian, but it's really in line with the Catholic tradition"--or something to this effect. I even saw the acknowledgment section of an article in aPoR where the author thanked two other philosophers from saving him from heresy.
I have a recent qualitative study that just appeared in a special issue in Res Philosophica on new approaches in philosophy of religion (last non-copyedited draft here). I surveyed philosophers of religion and found a solid 61.1% were Christians. They explicitly identified with Christian orthodox statements, such as the Nicene creed “I am committed to the central claims of the Christian tradition, captured in the Nicene Creed,” “I affirm the Apostle’s creed and the Nicene Creed. Beyond that, while I have opinions, I regard things as pretty unsettled and tentative.”
In a straw poll among my aPoR friends on social media I likewise found them to be mostly in line with Christian orthodoxy. I asked why they went with such teaching, and why there seemed little appetite for non-orthodox ideas (I am not using the term heretical here as it carries a negative connotation). The main reason seemed to be that these philosophers trust the Church (what the Church is of course varies, it can be the Catholic church for Catholics, or the Anglican church for Methodists or Anglicans, or something broader such as topics that Christian churches consent on before the great schisms).
One could formulate an argument along the lines of Linda Zagzebski's argument of why it is proper to defer to expert testimony, or testimony of something or someone that one considers to be superior in knowledge than oneself. Her track record argument says that on the whole, I will be more wrong (have a worse track record) than expert E in domain D if I follow E some of the time, then I will end up with a worse record getting at the truth. Therefore, I should follow E on matters in D all the time. So given the accumulated (possibly divinely inspired) wisdom of the Church, I should defer to church tradition rather than pursue discredited viewpoints such as non-Trinitarianism, Docetism, Arianism, etc.
While this may be individually rational, I cannot but help be a bit uneasy with all this orthodoxy. For one thing, if experts to which we defer show more epistemic individualism, the conclusions they reach--if they concur--will be all the more impressive. Finnur Déllsen recently made an argument along these lines for scientists (paper here): it is better if scientists adhere to something like the enlightenment ideal of autonomous inquiry. Their joint independent testimony provides a Whewellian convergence of induction, which makes it more reliable for laypersons.
I am reminded of one of the earliest philosophical novels, Ḥayy ibn Yaqẓān written by Ibn Tufail in the 12th century. In this story, a boy (Hayy) gets raised by gazelles on an equatorial island, and he comes to a wide range of beliefs through personal reflection. These include beliefs about astronomy, botany, and anatomy, and also about religion. Hayy formulates several cosmological arguments and comes to the conclusion that God exists, and that God is one and indivisible. It would surely be impressive if people would come to monotheistic religious beliefs completely independently of each other, and would greatly strengthen the case for monotheism. As it is, monotheism is not an independent invention. Most of the world's monotheistic beliefs stem from a common source.
All this doesn't detract from the fact that joint testimony can be more powerful even if it isn't independent (as Lackey for instance argued happens when several experts believe the testimony of another expert). But independence and consilience of induction does mean that there is value in unfettered philosophical inquiry, even if it were to radically deviate from church teachings.