so you have it exactly backwards. or maybe not, who the hell knows with hegelians.
Also..I read the book of Job, supposed to be super-impressive. OMG. God comes over as such a twat, is dicking around with Satan, makes a stupid bet just because Satan wants to, to torture the apparently faithful Job.
Well, Marxism has a lot of similarities with Christianity, as has been pointed out by a lot of people. So maybe 'that' kind of atheist mostly comes from replacing one's christianity with another religion. Ohh sure, "becoming an atheist" means you used to be religious, I guess. But there are other religions. Thousands and thousands.
Religion has elements of ideology, some ideologies are derived from, related to, or specifically opposed to religious belief. That last might be an XOR.
In the non-jargon common sense of ideology ("a system of ideas and ideals, especially one that forms the basis of economic or political theory and policy", thanks dictionary) you're broadly right.
Like a dictionary? It's just semantics
If you remove all the cosmology and mysticism from Buddhism, you are left with something other than the original practice.
But you can approach religions as a topic in countless ways, so I think it is fair not to reduce it to the lowest (albeit maybe most common...) approach people have