Question

How do you think the belief that a person could be reborn into a different caste system affected the way people lived in Ancient India?

Answer 1

People born into lower castes must have been unhappy about it and feeling a lack of fairness. If they did not have a hope for a better life, they could have rebelled against the system. Further, those from the lowest spheres of the society sometimes would have nothing to loose if they rebelled. This would make it even more likely that they could rebel.
The belief that if they accept the current situation gave them a hope that they could actually  have a better life in the next life. This  kept people from rebelling and maintained security and stability