this site is for this kind of question, so... good job!
there are lots of different theories about what would be (and what would get to) an anarchist society. some of the components you mention, egalitarian religion and self-managed production/labor, are specific to one branch of anarchism.
as to whether all anarchists support the total abolishment of the state--it depends on how you define the state. some anarchists think that there would be lots and lots of meetings, based on neighborhoods or regions and/or types of work. others think that people would live in smaller groups, so there would be no need/desire for wide-spread systems of conformity.
people have always lived in groups, and we have always had rules that we lived by. we don't need a government for social rules. how do we know now that our values align with our neighbors? either we're friendly with them and we talk about stuff, or we wait til there's a conflict, and then we figure it out. what that "figuring out" would look like in an anarchist situation, again, depends a lot on what kind of anarchist you are. some would say that the neighbors would get together and talk through the conflict, others would say that the two households can deal with it how they like until/unless it affects more people... and others would say that if people are living in communities that depend on each other for their lives, then the kinds of conflict that would arise would be really different.
i hope that clarified something, leaving room for the reactions of anarchists who disagree with each other can lead to some vagueness. :)
edit: to be clear, anarchy would mean an end to capitalism, since capitalism is exploitive and can't really be broken into pieces of ok and not-ok. (that's the definition/understanding of capitalism used on this site, and that i think makes sense.)