Are they not both just collections of agreed upon theories?
No, they aren't. Religion has a hypothesis, that under any reasonable test fails. Religion postulates and asserts what it cannot possibly know.
Also; What is your basis in denying an others evidence (anecdotal or otherwise) from their choice?
Anecdotal evidence is just that. I really don't need to say anything more.
So, science doesn't postulate things it can never know and if it doesn't happen in a controlled, repeatable environment it's invalid.... interesting.