on the basis of the forms and types of evidence being mobilized
I actually do think this is part of the problem. For me, we haven't even gotten to the question of evidence. Religious "knowledge" is based around non-falsifiability of certain doctrines and axioms. Even within their own epistemological frameworks they have non-falsifiable arguments. This is fundamentally at odds with scientific process which must be fundamentally falsifiable.
Religious disagreements are fundamentally different than scientific disagreements. From an epistemological core they are different. Either things are falsifiable or they are not. I would go so far as to argue that religious arguments typically are epistemologically unsound for this reason, regardless of evidence.