The questions asked here are loaded with presuppositions which ought to be questioned and challenged. Otherwise, how are we understand what is being requested, if anything at all actually is being requested.
What is evidence?
What is a theological claim?
What is reality?
What is an aspect of reality?
What is an explanation?
How do you substantiate an explanation?
The answers you give to these questions can easily make the questions you have posted either nonsensical or trivial.
Evidence apparently means different things to different people in different circumstances. Personal experience is generally taken to be the strongest sort of evidence for personal belief but not very good evidence for convincing other people to agree.
If a theological claim is a claim about God then the first theological question to answer would be, what is this thing you call God?
Is reality something other than what you experience? If so then why are your experiences to be considered not real and why is this reality you do not experience to be called real?
What does it mean to say a theological claim is an aspect of reality? The claim is real, so is the question whether the claim is regarding something real? That of course would depend on what you think the word “God” is referring to. If it is about the content of book or about what people are thinking then does then how is that not an aspect of reality?
People seem to expect very different things from an explanation. Explanations which satisfy one person often seem to do very little for a another person. A scientist tends to expect an explanation to provide some means to test hypotheses, while another person might consider such explanations to be meaningless and they want something that makes sense of their experiences.
This suggest very different ways in which people would substantiate their explanations. Some will be listing their experiences while others would be making measurements.
To me it sounds like a reference to an anime series entitled “Mushi-shi.”