I think any view of life consistent with its emergence by evolution isn't consistent with reincarnation, or certainly doesn't support it.
But given the universe in total may be unimaginably larger than our observable universe, and the total universe may well be an insignificant feature of an unimaginably larger reality, its quite possible that versions of us appear in a fractal-like way, over and over across reality.
Also, given the many worlds interpretation of quantum mechanics, which is the most basic (Occam's razor) interpretation of the equations, we are constantly spinning off a foam of combinatory alternatives of ourselves and everything around us, because the particles that make us up are doing that. So we live many lives, and even when we die in one perceived timeline, other versions of ourselves continue their journey.
Both of those are scientifically plausible, especially the second - which many scientists already believe to be true.
Although they sensibly tend to focus on interpretation at the particle level, avoiding the hype and wishful mysticism that would tend to crop up around its implications for us as individuals. Too many imaginative people and popularizers have a tendency to jump from actual equations/constraints they don't understand, to non-scientific psychologically motivated "implications" and ideologies. Quantum mechanics has been abused enough that way.