In this paper (full text available below), Jim Downard tackles non-overlapping magisteria, or NOMA. His summary follows:
Make no mistake about it, this non-overlapping magisteria (NOMA) issue is one of the prickliest ones in all the religion/atheism debate. ┬áThe historical examples of Clifford, James and Russell are used to lay out the argument without jabbing at some of the current combatants in this area, but that shoe is naturally waiting to drop.┬á The upshot: Gould got it almost right.┬á There are Non-Overlapping Magisteria, but the line isn’t between science and religion as he thought, but between decidable (scientific) knowledge and undecidable (philosophical) beliefs.
Unfortunately, all too often the┬álandscape of things that are true or not is seen by many atheists and religious believers alike as essentially a flat terrain governed universally by whatever┬álogical tools they deem appropriate.┬á The atheist gets in their bulldozer and, fueled by sufficient evidence and sweet reason, intends to push all religious doctrines over onto the false side.┬á Meanwhile, the religious logician, armed with their revelations straight from the Designer’s mouth and bags of Intelligent Design “scientific evidence”, is equally confident that they can plow all materialist naturalism onto the same false zone.
Viewed from above though, along the scholarly methods catwalk snaking overhead, you can see both sides have slammed to a halt, and can’t seem to accept the idea that their respective dozers┬áhave gone wheel spinning because they have slammed into the NOMA barrier isolating decidable from undecidable questions.┬á It is not at all pleasant for some lovers of clear thinking to realize┬áthat scientific reasoning and philosophical reasoning share many logical tools in common, but are fundamentally different ensembles that cannot be applied automatically across domains.
Pure logic and scholarly method are still available for use, running along that catwalk overhead, but have their own limits that must always be kept firmly in mind.┬á┬áAristotlean logic can tell you that a┬áconclusion either does or does not follow from a premise, but cannot tell you whether the premise is itself┬átrue or false.┬á Likewise, scholarly method can establish that Smith was or was not validly quoting Jones on elephants being a form of asparagus, but this┬ádoesn’t give you insight into whether elephants actually are or are not a form of asparagus.
Ideally, as much traction as possible should be obtained along the logic and methods catwalk, but eventually you have to drop a rope ladder down to the contentious ground.  It is necessary then to know which reasoning tool kit to pack along, based on which side of the NOMA fence you intend to land on.