Religion, and ideology, are loaded terms, difficult to define clearly, dependent on context, and frequently used pejoratively for whatever some other people do, not oneself..
Popper identified commonalities between Plato (who's thought actually underlies a lot of the metaphysics of Christianity as very much distinct from Judaism) and Marx. He does this, in declaring them Enemies Of The Open Society in that book. And many others have identified superficial commonalities between Marxism and religions. Few between say Rand's ideology and religions that require sacrifices to propitiate deities, though surely that case can easily be made.
Your characterization of Christianity seems, untenable. There are some comments about rich men and the eyes of needles, but that has to be understood in the context of spending rather than hoarding wealth. Christianity sides with those who uphold the correct creed, rich or poor, and everyone else can literally go to hell. Liberation Theology is sometimes described as a return to the values of Jesus, but more often as synchretism with communism.
You have to proceed carefully, with a clear definition of religion, narrow definitions from within cultures or practices, or broad anthropological ones that include say sports and hobbies.
'Catch on' is misleadingly vague. Communism was a popular philosophy across a chunk of the world, as was Liberation Theology. What is notably different is that one inspired Lenin's fanatical faction to take totalitarian control of an empire, while the other was ruthlessly suppressed with funding from the USA (although Pope Francis could be described as inheriting it's radicalism). Does that tell us anything about the ideas? Only their utility for taking political control. And that in fact, led communism to fail at achieving it's declared intentions, while arguably Pope Francis manifests a change in the discourse that political gains could not, like say in Venezuala..
In terms of driving energy of the popularity of egalitarian ideas, the book The Spirit Level makes an interesting and strong case https://www.goodreads.com/book/show/6304389-the-spirit-level The poor in rich nations, suffer harms that the rich in poor nations do not even where their absolute standard of living is lower. They relate this to human biology and the social development of the brain, and the egalitarianism to which we evolved.
It is interesting in this light to consider the massive and accelerating rises in inequality in recent decades, and the potential for this to drive instability - as indeed may have influenced the fall of the Roman and White Russian empires. Many say the real core of Marx's analysis, and the lingering and difficult to answer problems we are still posed with, is the issue of https://en.m.wikipedia.org/wiki/Surplus_value especially in light of the social infrastructure for increases in this.