From what I gather, they're saying CSR needs fine tuning in terms of recognizing the neural correlates of a given religious belief?
Yes, it does, mainly in the area of reproducing study results for ongoing verification of earlier findings. This doesn't necessarily vitiate whatever findings are coming at us from neurological studies related to human belief functions of the brain, but it does impinge upon the assurance and the breadth of applicability of the findings. We can't just take a single study's findings for granted, nor can we assume that some specific finding necessarily explains some social context or psychological context in which a belief process takes place.
Right, religious belief is not mere belief in a set of fact claims. It has intentionality, in terms of how one approaches life. I can say I believe claim x, and let's say I do, and yet how I approach life might be in no way reflected by that mere belief.
Yes, there is that possibility. But as I was mentioning earlier, where 'Christian belief' is concerned, there are epistemic considerations expressed within the text of the Bible that, whether any of us feel we likewise recognize these epistemic structures in our own religious understanding or experiences, are inherent to the content of the Bible. These can't be simply ignored and then dismissed by saying they are inconsequential to the Christian status of a Christian belief, trumped by modern neurological studies or even secular philosophical considerations regarding human belief
On the other hand, I can be doubtful about a particular claim, and yet still approach life as if it's true. Let's say, I have heard, but am doubtful, that God loves me and created me to live in a particular way, a way fitting to love (perhaps I'm supposed to love and care for others, as they say God does for me). In this case, my credence level is low, but I still try to live accordingly.
Sure, there's the observational and experiential sense data that come by interacting with Christians who claim they are being guided by God, but there is also the idea that God has some volitional influence within the activation of at least some Christian beliefs. There are also the factors of social psychology that inform the overall confluence of belief formation, often accompanying various social and educational endeavors. So, a marginal belief that just 'can't be had' in one passive setting might become a more substantive belief if fostered or searched for in a more active, ongoing scenario involving the same person.
Religious faith, Christian faith at least, entails an element of trust that can outpace the propositional attitude of belief. Jesus seems to imply that the reception of revelation (strong belief) in some sense depends on an intentional approach to life (John 14:21). But even in the one who has strong belief, they still must get up and go through their day trusting the one in whom they believe. It's that personal element of trust that is inescapable, even with a high credence level of belief.
This is true, PH! The social psychology of trust needs will play a part in influencing the direction and the felt motivations one feels to 'chase after' either a fuller data set for possible Christian belief(s) or to instead 'chase after' a fuller data set for possible ideas that militate against Christian belief.
Either way, it's my contention that most people are acculturated into a path of belief or unbelief through active social means, means that are deemed to be either socially or epistemically trustworthy (i.e. attending church and/or reading books, engaging educated sources); and they don't believe or not believe an idea by just passively being struck by random ideas or strong notions while sitting on a chair, staring out of a window. So forgive me if I think this whole paradigm that sees 'belief' as utterly involuntary to be at least partially spurious.