That is the thing about a cult, it is not rational. They believe in an afterlife, so this life doesn't matter, it's just an 'illusion'. So, killing everyone is not a big deal, since they will all just wake up together and happy in the next world, which is so much better than this one, and we know this because ...reasons.
Sadly, this is all too common, not just in fiction but even in the real world. The worse people have it in life, the more likely it is that they will develop some kind of afterlife to justify their suffering.
Now look at this world, not only is it horrible, for the normal citizens, but it's even harder on the wastelanders, and they both have it easier than the mutants. They have been doomed to die early, they are shunned by the citizens, can barely get food, have to pay taxes (if they are in the city), and can't do anything about it. It only makes sense to have a nihilistic attitude, and faith in a death cult promising a better life.