If that's the case, she should see a god which really does hate homosexuality, eating pork, and considers working on the sabbath worthy of death, or wants the whole world to live under Sharia law, as equiprobable with one that loves everyone. She most likely behaves as if she had some means of discriminating between supernatural hypotheses even if she disavows being able to.
Have you read What the Tortoise Said to Achilles? It's reprinted in Gödel, Escher, Bach: an Eternal Golden Braid.
From Being a Realist (even if you believe in God):
My mother, who doesn't call herself a theist (I think she's agnostic), doesn't even accept realism. She doesn't even agree with this:
That's little more than tautologies here. Yet it elicited an impression of being forced to believe. I know because she told me about the totalitarian dangers from such narrow thinking.
I'm happy to have finally found the root cause of our ongoing disagreement, but now, how can I deal with that? It looks pretty hopeless, but just in case, does someone have a suggestion, or should I just leave it at that? (My ego doesn't like it, but giving up is an option.)
Now I'm relieved to know that in near mode, she's a complete realist. This craziness only shows up in far mode.