As religious faith has declined, ideological intensity has risen

An alternative view, and one that, IMHO, is favored by Occam's razor (to name just one cognitive tool), is that both religious and secular ideologies are consequences of a more general human nature.

Because there is a clean distinction between athism(not relying on belief) and antithesim. Scientific method is a lens of analysis tool and it's beyond the framing of belief as how religious people claims, or even how antithesim people claims. Just like how I would explain the same to the some antithesim group that science doesn't prove the god don't exist. That's still a misuse of the tool of scientific method. To believe the opposite is still a belief, and missing the mark of the scientific method where the most important part is the process not the result.

The label "not religious" doesn't mean anything. People use it to refer to atheists, in which case you are alleging that atheists by definition don't have the tools to understand their own position - which is absurd. Others use the term to refer to minimally-practicing members of a faith who basically only show up to places of worship when there is an official event, in which case you argue that these people don't understand the reasons why they avoid their own religion until they become active practitioners.

> The secular world would benefit from adopting more formal definitions of their belief system.

First of all, a secular world doesn't preclude the population from being religious. Having a secular world that is explicitly separate from religion only means that society itself is not regulated by religion.

If by secular world you mean the percentage of the population who is atheist or agnostic, then you're not talking about a specific belief system. You're talking about a diverse group who have chosen to not believe in deities, and that often extends to not believing in the supernatural altogether. The allegation that this absence of belief happens without reflection is simply untrue. On the contrary, being an atheist is still a thorny path to take, even today. It doesn't happen passively.

> In the secular world these aspects exist but they are implicit, making them difficult to debate and attack.

When you say that these aspects are well codified in religion, what you really mean is that specific religions have behavioral codices that members must adhere to. The consequences of non-adherence depend on the religion and the society. But when you look at different religions, these codices are all quite different.

As soon as a population contains more than one religion, what you are touting as a benefit quickly becomes just as impossible as if you were dealing with an atheistic society.

What you find difficult to debate and attack is non-uniformity in general. I consider that a plus.

You are of course completely correct that a diverse society can appear more nebulous, and in some ways individuals can have a much harder time finding a path in life if they, well, have to actually go and find a path. This is a consequence of the freedom to choose. Systems that don't give you those freedoms are assigning a path to you from on high, or at least they heavily constrain your choices. No doubt some people would prefer that.

But the benefit of living in an open society is that you have the option of choosing to be religious, and you are free to choose any religion and any flavor. A secular society doesn't take that away in any form, it just means that your religion doesn't get to make the rules for people living outside of it.