Making the case by using sophisticated work-arounds like concepts such as past lives may seem like an eloquent way to discuss possibilities (incredibly unlikely ones at that which seem more like an ad-hoc hypothesis than anything), but when you look at the concept on a practical level, such logic is utterly abhorrent and has no place in human society. Take Hinduism for example.
For many years in India (and to some small extent today even) ignoring the issues of the poor was justified by religious logic. Hindu moral principles and the idea of karma holds that people are not born into their station in life arbitrarily, but based on actions in their past life. Thus no one is unfortunate enough to be born poor, they're born poor because they were bad in a previous life. Not only does this make no sense because the "first life" initial conditions of humanity still had some people elevated above others even when the karmic slate was clean (not to mention social mobility is the antithesis of this concept), but it leads to lack of sympathy for the poor. After all, if they put themselves in that position, why should I help them?
They're suffering because of evil actions in a past life and it's up to them to live a good life, gain good karma, so that they can be reincarnated at a higher level. And of course Hinduism isn't the only branch to employ such twisted logic. Calvinists have their own deterministic nightmare.
The problem here isn't with religion in general. There are an infinite number of potential religions that could be true. I'm not one to make statements about the impossibility of anything because I know how hard it is to prove a negative. It is however, difficult to deny that certain claims are more far-fetched than others, and (in a classic Saganism) extraordinary claims require extraordinary evidence. I find a lot of the claims that are often made by popular religions to be contradictory. For example:
God is all-knowing, yet god has granted human beings free will. If god knows what decision is going to be made before it is made (which is required under omniscience) then how are human beings capable of free will? Isn't that predestination?
God is all-powerful, the source of all things, perfect, and omniscient, yet evil exists in the universe. For reasons stated previously, this too seems contradictory. Especially when that evil doesn't arise from entities capable of free will.
Going back to my original point, there are plenty of religious theories and configurations that get around these apparently problems. If you don't believe in a perfect god, that fixes nearly every problem. If you don't believe in monotheism, there's another easy fix in most circumstances. We're not discussing all religion in this thread, just those that are victims of this dilemma, because they aren't subject to that dilemma.