Your recognition of explicit vs. implicit ideology is addressed by Slavoj Zizek in some of his work. He generalizes ideology to be mostly a set of assumed or unstated beliefs and ideas which are so internalized they are not even consciously recognized. Could be good further reading for those further interested in the subject:
https://en.wikipedia.org/wiki/Slavoj_%C5%BDi%C5%BEek_bibliog...One of the main points of Zizek regarding ideology, relevant to what you said, is that as religious ideology has waned in importance, other ideologies have taken their place, yet because they do not come from religions we do not recognize them as ideologies, though they are. But ideology has always existed in this form, in the background. It is just without religion taking a forefront in life that the importance of other ideologies has grown.
Anyway, I bring it up because I do not think it is possible for us to explicitly address all ideology. Ideology is part of the human condition, not in a metaphysical sense, but because we have only limited abilities to perceive and understand the world - finite lifetimes, limited senses, limited cognitive abilities. We must make assumptions and generalizations, take things for granted, and trust people and ideas so that we can spend our time thinking about other things.
Why? Because it's exhausting to explicitly address all ideology. I'll give you some examples: Country, Culture, Government, Justice, Love, Fairness, Ownership, Work. In discourse we take on only limited slices of what these concepts mean, yet we take their existence and high level concepts for granted (though one person's concept of fairness may not match another's). These are heavy, complicated topics in themselves.
> If you believe you are not religious, it just means that you don’t have the cognitive tools to recognize the secular ideology that you have adopted.
Depends on how you define religion. In my opinion what separates religion from philosophy or just ideology, is claims regarding the supernatural and divine. You can absolutely appreciate religions for their wonderful philosophy and theology while rejecting what I would consider very core parts of what makes one a believer in a religion, like belief in supernatural events or divine beings.