How is their religion directly responsible for their poverty and overpopulation?
I'll briefly explain it.
The caste system is deeply ingrained in Hinduism; a system where only a small percentage of Indians (Brahmins) are privileged, and the rest are in lower castes. In the lowest caste, until recently, the religion demanded that the people could not be educated, could not work, should not be fed.... If they were starving in the street, they should be overlooked because it was their "Karma" to be poor.
Reincarnation is involved in the problem because it elevates the honor given to certain animals. For example, rats could be humans in another life, so they cannot be killed. If they are eating the grain (and they do), they cannot be stopped, so that the humans who need the bread from the grain die of starvation.
And it's part of the religion.
The religion also causes the pollution. The Ganges is "sacred." They toss dead bodies in it. They toss sewage in it. And they bathe in it and drink it. It causes disease and death.
Hinduism is directly causal to the poverty in India.