In relation to modern science, I think it is better to focus on the more basic problem of whether subjective experience is reducible to physical phenomena. If consciousness were to be accepted as a basic aspect of reality, then this would open up all sorts of possibilities, including, potentially, rebirth. For mainstream science I think the time has not yet come to seriously grapple with rebirth.
And, yes, there are clear causal connections between the physical and the mental. Yet how this should be interpreted will depend on what we take to be the basic building blocks of reality.