In What happens to non-materialists about consciousness?, I tried to show how non-materialists about consciousness can hardly stop there, and will need to accept that other phenomena in the nature as life and evolution are not-fully-physical also.
In my thinking, there is only one rational way to combine those things, without getting into dualistic thinking. And that is – to consider physical-world-of-physics a projection. In sense simmilar to that of vector space projection in math.
The analogy would be this… the physical-world-of-physics would be the x-axis, and the real world would be the plane. Analogical to the projection (in the example P(x,y)=(x,0)) would be the quantification of abstractions by 3rd person observers used in physics. This should be taken merely as analogy, as the projections in math are always quantitative in nature. Not so in the case of world to physical-world-of-physics.
So mind and brain would be two projections of the real world, one into 1st person abstractions, and the second into 3rd person abstractions. And because they are projections of the same “reality”, they show correlations. Of course, nothing is special about the part of reality which is projected to brains/minds, so it would be true that there would be something missing out from our analysis of projections of life, evolution, and everything else.
Of course, for one to accept this kind of thinking, must accept that things are not configurations of parts, but that things which exist can be further determined somehow. Check the semantics posts for argument on this.
And this is compatible with physics too. Take for example quantum entanglement which is more compatible with the idea of existing whole, which can be further determined (collapsed by measurement), then to usual thinking of physical systems as configurations of parts. Stanford encyclopedia has nice article on relation between physics and holistic ideas in general.