If your position is that brains are not actually bound by the laws of physics -- that they operate on some other plane of existence unbound by any scientifically tested principle -- then it is not only your ideological opposites who have quasi-religious faith in a thing not fully comprehended.

My "position" isn't remotely that. The problem with "brains are bound by the laws of physics" isn't that there's something special about brains. It's that physics doesn't consist of "laws" that things are "bound" by. It consists of theories that attempt to describe.

These theories are enormously successful, but they are also known to be variously incomplete, inconsistent, non-deterministic, philosophically problematic, open to multiple interpretations and only partially understood in their implications, with links between descriptions of things at different scales a particularly challenging and little understood topic. The more you learn about physics (and while I'm no physicist, I have a degree in the subject and have learned a great deal more since) the more you understand the limits of what we know.

Anybody who thinks there's no mystery to physics just doesn't know much about it. Anybody who confidently asserts as fact things like "the brain consists of protons, neutrons and electrons so it's impossible for it to do anything a computer can't do" is deducing things from their own ignorance.