I believe in social norms for the inherent sake of the norms, rather than due to doctrine. I jettison no norms - only doctrine. Philosophical systems are orthogonal to theological ones. If there exist implicit beneficial norms associated with Christianity, as you say, then I posit their implicitness implies they can be disentangled from theistic ideology and the case can (and perhaps should) be made for them outside of such systems.
If you think another attempt would be successful, that you, or another cadre of well-intentioned reformers, can successfully inoculate a society with an abstracted ethical code that mandates returning evil with good, embracing the martyring of oneself for truth, total pacifism, etc. on a purely logical basis, by all means go ahead and give it your best shot. Until then, I'm going to loudly proclaim that Chesterton's fence should be returned to its field.
The cause is the same force that drove McCarthyism and other forms of tribalistic insanity. Blame humans, not individual human groups or ideologies. I have no problem with religion, but I strongly disagree with the notion that society is, as you suggest, necessarily held together by the social norms of a particular instantiation of organized religion. It's perpetration of the same ostensibly righteous style of judgment that this article seeks to criticize.