So, given that chemistry plays a huge role in how the human (or any) brain works, it would be quite a stretch to argue that the brain works with classical physics.
We are often sloppy and sort all the chemistry in with classical physics, but that's a very human-centric approach. In reality, the Universe doesn't have different "domains" with separate rules for chemistry and physics; it evolves according to the Schrödinger equation, and we use Chemistry as an abstraction to not have to deal with nasty mathematics to predict how certain reactions will work.
It’s been almost entirely based on maths and careful measurements from machined instruments purpose built for observing phenomena.
So at this point you’d hope the limitations of our biological senses would have been long surpassed.
We can try to retrain and reuse the sense for other purposes though. I'm reminded of that film "The Zero Theorem".
Neural nets are called universal approximators for a reason. If what you guys are discussing is true, then a neural net would not be able to learn from a dataset about quantum experiments. I doubt this is the case. Also there is quantum cognition, and by that I mean the fact some researchers figured out a lot of puzzling results from experimental cognitive science seem to make more sense once analyzed from a quantum perspective.