"Put another way, this is the premise that the mind arises out of ordinary physics... If you are very religious, you might believe that a brain is not possible without a soul. But for most of us, this is an easy premise to accept." The thing that irks me about this is how it reinforces a common (and in my opinion, false) dichotomy: either you believe the mind is explicable in terms of ordinary physics or you believe…
That's just vitalism: https://en.wikipedia.org/wiki/Vitalism Either everything exists in the material world, or it doesn't. There's really no way of avoiding that binary. If you think there's something else, that is by definition supernatural.
First, how others perceive your words usually matters more than the precise definitions you have in mind. If I describe myself as believing in the supernatural, it has a lot of connotations I don't want.
Second, the possibility that consciousness (in some sense) could be built into physics themselves. So it doesn't contradict that the brain is made of subatomic particles, but the workings of the universe have more correlations built in that could work at different levels. Something I think is comparable is that many cosmologists think that the arrow of time, which events come before which, can be explained by a universe with initial conditions of extreme low entropy. So there's nothing within the universe that explains why the initial conditions were like that, but it's a real property of our universe.
Maybe consciousness could be an end state that the universe is progressing toward. Is that really so much weirder than working from an initial state of extremely low entropy?