At least flat earth is well defined. We can describe an experiment that flat-earthers would agree in principle would determine one way or the other if they are correct, nothing like that exists for consciousness
Indeed, there is a lot of flat earth like belief that there must be something beyond physics or turing computability in a human brain.
Well, there is quantum stuff affecting synapses in the brain. So at least there's something beyond "classical" physics going on.
I did not say "classical" physics, I said physics. Quantum phenomenon are part of everything. If you mean quantum phenomenon have non-trivial effects on human brains, as far as I am aware thats not proven but its not a problem as its well, natural physics.