I used to be a duelist too, back when I was more agnostic than I am today. Now I find it hard to understand the epistemology of an atheist who is not a naturalist/materialist.

Generally, atheists who are not materialists base their position on attributes of consciousness that are hard to imagine a materialistic explanation for. For example, you are having a conscious experience of a computer screen right now, and that experience appears completely different from a chemical reaction, as do mental phenomena like beliefs and emotions. There are a lot of other aspects of consciousness like this, e.g., your belief that the Eiffel Tower is in Paris is about the Eiffel Tower, but it's hard to imagine how a physical process could be about something (this is called intentionality).

Materialists respond by saying that we will reduce all of this to physics and chemistry someday, and materialist philosophers have also raised interesting conceptual points, but dualism is clearly a reasonable position at present.