Hindus believe in reincarnation ( a progressive journey towards the higher existence). But Karma comes into play, bringing I guess, moral in the picture. One note is that they believe that the soul is all existing not influence by birth or death ( which applies only to the physical body). And based on individual moral choices, the spiritual elevation of the soul's journey towards the supreme is either closer to or sets it farther away from the all pervading spiritual existence.
Reincarnation is influenced by our moral choices, as being reborn as a human with the capacity to choose to get closer to the supreme soul or energy is considered to be the most precious gift to the soul and the final stage of rebirths, as this is the unique opportunity to achieve what should be liberation from mundane existence and into blissful spiritual existence.