Why "extraordinary claims require extraordinary evidence" works with feelings about the divine.

You cant truly "know" forms or relationships between them (also forms), because experientially they are not fundamental. All things, including logic and reasoning are experienced as feelings with varying levels of quality (depth), thereby you dont conclude something by "knowing" but by feeling. Thereby if any feeling is experienced as extraordinary proof of something, it is extraordinary evidence for the experiencer.

We can hold something as evidence of something being real for ourselves based on the quality of the feeling. Reasoning lets say that materialism is true itself is a set of feelings, if a feeling like the feeling that god is real trancends that, it appears as more real.