I dunno about non-locality being non-secular. Gravity is an example of non-locality, action at a distance. Newton described it in a way that explained his universe, and I suppose that it works still for most of us in our daily lives. I guess I am missing the spiritual aspect of stuff falling down. But if you'd like to discuss spiritual aspects of Bell's Theorem or Werner states or non-local Lagrangians, I'm all for it.
The behaviour of a single photon is interesting under certain conditions, even unexplainable with our present knowledge, but it doesn't change my life. Our mental model of the universe, from Copernicus to Newton to Maxwell to Einstein to Weinberg to Kaluza, has long passed from things we experience with our senses into the esoteric realm of quirks and quarks, bozons and neutrinos. These understandings may be profound, and lead to other more profound understandings, but the mental model of the universe we must carry with us need not follow every development at CERN.