Religion is what keeps the poor from eating the rich
Not just that, but religion helps normalize a lot of the problems of neoliberal commodification, for neoliberalism depends on social dualism. In layman's terms, so long as one thinks things can be isolated, we can be propagandized into seeing problems not as systematically cultivated, but just personally private.
You don't have to look far to see someone assume poverty is a lack of character, do you? Religion has actually helped this idea get normalized, because it asserts the granddaddy of isolationisms: a separate soul from the body. Doesn't take too much to see a society, even secularly, assert man is an isolated bugbear with free will. These are dangerous positions, and as you alluded to, part of the reason the masses of people suffering don't "wake up" to the trick played on them. If we can take systemic problems and simply say they're standalone, that right there cripples a response, and this has been the GOP's tactic for 30 fucking years.