The sound secular position is that governments ought to have no power to coerce belief, or enforce lack of it. That was the principle on which our Republic was founded, and it ought to be the model for all the earth.
The short answer is that a belief in reincarnation is not automatically an endorsement of gods (or "devils", whatever they are), and so you can believe in reincarnation and be an atheist too.
Life as an organic replicator seems as good a shorthand one as any, though even if a particular organism is incapable of replicating (some defect in its biology) that wouldn't make it not alive, would it?
The notion that professing to lack belief in something presupposes you had to believe in the existence of that to begin with (and moreover, that the object had to be real also) falls completely on its face.