She sounds like the ordinary compartmentalized nutcase.
What you need to do is ask her why she doesn't act on her non-belief in realism, why she doesn't apply the far thinking to the near thinking.
When I gloss over most of the comments here, they are as hilarious as they are useful and true. Which is to say a lot. I love this community.
Jaynes? Didn't you mean Aumann?
Breaking the walls won't be easy, because she deliberately compartimentalize. So I'm not sure that pointing out that in "real" life, she acts as a realist would work. Most likely, she would say it's not the same thing, and that different methods of thinking apply to different situations. She denies the possibility of a unified principle, let alone the fact that we may have found it.
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.