I was talking about literally every social chaos algorithm I've ever seen. not one of them retains cohesive structure without a binding variable like religion or philosophy.
Take China as the biggest and most successful atheist nation ever in history. The Party has run into this problem on a massive scale time and again. They have repeatedly had to revamp their failed balance between engineered ignorance and forced indoctrination as religion has re-grown in large population centers without a massive level of heavily indoctrinated citizens in place. The entire Ughar problem is a current case-in-point. They're bussing in hundreds of thousands of Chinese nationals deemed acceptably "Chinese" by the state in order to break up the naturally evolving narratives.
Even with that tremendous expense (both direct and indirect as they try to whitewash what they're doing in the UN) they're still not really able to call it successful. The real problem is that in order for an individual to impose self-discipline they must rationalize it and without the cognitive tools to construct a rational narrative that is compatible with the requirements of the state fragmentation is inevitable.
When modeling social dynamics (the branch of sociology and mathematics that relies on chaos theory) there are multiple deterministic patterns that have to be modeled. People need food, water and basic resources as well as a sufficiently diverse gene pool. Moving past those as population increases one starts to require additional repetitive series and one of those is most easily described as memetics (
memetic theory) (the shared common ideas in a clearly defined cultural group). Chomsky made it popular but it's developed quite a bit since he first popularized it. As wikipedia says in the first paragraph: it's essentially information flow.
During development the minds of children face such a massive influx of complex interpersonal and social dynamics that they have no choice but to rely almost complete on guidance to arrange them into a cognitive framework. At first this is, in most cases, entirely one parent. As the child grows in complexity, however, they will begin to delegate some areas to the other parent or anyone else in their life they deem as more authoritative a source about one or another subject.
One can keep going down this rabit hole until one has mapped out a common series of memetic themes that are common across all individuals in one more more large geographically diverse regions (say... western cultural norms).
Thematic supercells: economics, religion, liberty, human rights, sexuality, etc...
Hopefully this is enough to begin with to start to see the big picture of how these models are constructed. Then one simply has to lay out some common sources of those thematic elements (religion, pop culture audio and video, public education, etc...) and then one can target and model each one and run the models.
Personally I'm rather proud of how my models actually pull in their variables for pop culture and regional religious themes from social media. I believe it makes them more accurate but enough bragging.
So, it's also simple to put in a condition where a major one is destroyed without significant changes to another and play the model forward to see what happens.
In every single one when religion is destroyed without replacing it with a state-sponsored religious replacement the social model fractures (breaks down into civil conflict) over 1-3 generations.
Thus: the Chinese are bussing in nationals to replace the Ugar. They have experts with models too.