You fall into a trap of using a single English word to cover a multitude of different world-views. It would be as useful to say that the quote "... how people present..."
Within the broad category of "religion" you have thousands of different groups, most of which would find minor, or very major, things to disagree on. Judaism is massively different to say Druidism or Buddhist. Crumbs, _within_ Judaism you have a full spectrum from Ultra Orthodox to unpracticing.
I would thus caution you from viewing the world as falling into either religious or irreligious. Ultimately that classification is not meaningful.