There are ways to have a conversation and there are ways to talk past each other. If you can’t imagine what it’s like to believe what the other person does, if you can’t take that subjective experience seriously, you won’t be able to reach most of those people. This is an important conversation because our beliefs and values orient our behavior and habits.
Atheist and religious folk are making incompatible claims about the way the world works and hence our place in it. The non-overlapping magisteria notion is hogwash. There was never an unbridgeable gulf between facts and values and never could be. Values presuppose facts about the world and the way that it works, i.e. your values can assume things that aren’t true (facts about human nature, for example). If a value is premised on a falsehood its expression can cause unnecessary harm.
The fact of the matter is, although we presuppose our notions about the world correspond perfectly with the world as it is, this just isn’t so. So what we are talking about when we’re talking about atheism and religious belief are our notions and how they relate to the world.
Some religious folk seem to believe that some personal experience internally labelled “divine” or “God” is evidence of an external objective deity of some kind (most likely as evidence to support the existence of whichever particular deity of whichever particular mythic tradition they’ve been steeped in). Evidentially speaking it does nothing of the sort.
Some atheist folk, never having tasted a “mystical” experience, have no notion of what it might feel like to experience something reasonably called “divine.”
In both cases people are talking about one’s experience of reality, and usually unjustifiably assuming a whole lot more.
These come to mind: