How, then, does God relate to human beings in a way that transcends belief?
In my book, God's interaction with humans is almost entirely qualitative. Everyone's personal information (material and immaterial info) is fragmented qualitatively. The false is always at war with the true. God interacts with us in immaterial realm as pure truth, which means He interacts very faintly with human truthiness (a Colbert term, I think), whether religious or not. This is a merciful thing, the Bible's full of language equating the purity of God's essence (Truth) as a "fire" which destroys falsity (kindling). God's a roaring fire of pure truth, which is why He interacts from a distance for now.
The relationship between any human (religious or not) and God boils down to interactions between these contraries, true and false imo. All humans are regenerated (false elements destroyed and reborn true, hence death and resurrection, the greatest metaphor of Christianity. In time all enmity against God (falseness) will be melted off (refined as through fire, 1Cor 3:5-11 and lotsaother verses from practically the entire OT) at which time hatred for God and all others (also hatred of the ideas of others) will be replaced with the harmony, communion, coherent interfacing, love, etc. common to the true.
The Bible promises this to all people by Jesus' atonement, but few see it because folks disdain the communication type God choose to reveal it in (allegory). Those of us who hate more will burn more, but the burning itself is ultimately salvation as it kills the false and God replaces this with true offspring. Cycle of [spiritual] life and all.
Unfortunately, most of my fellow Christians can't abide the fact that God treats all alike because the literal leads naturally to an elitist (and literal) rendering of a spiritual (allegorical) book.