Once you don't believe in souls and do believe in a random world with the quantum effects that mainstream science assumes as true, you have believe in life after death.
Considering an infinitive time of being dead very small chances are enough to get reincarnated sometime in the future.
To not believe in reincarnation you have to believe that there is something special about a human that isn't created randomly like a soul.
But if you do believe in souls, you do also have to believe in a mean God to not believe in some form of reincarnation.
So whether or not a soul exists, it's resonable to believe in reincarnation.