I can't say that I think either morality or moderate religious belief is truly about absolutes.
As a child I was subjected to two forms of religiously-run school: the first was a Catholic one, dependent upon French and Swiss priests. As my family and they were Europeans living within an Indian context, as with all expat communities we got to know each other quite well as people, not only as figureheads. I can't remember religious indoctrination from them at all, but I do remember a lot of friendship, and one priest even spent the time some afternoons after school to take me down to the beach and get me swimming. (I owe him. It later saved both myself and my wife.) They also held a large library of books of all types, detective yarns included, and it was through that resource that I picked up on Lemmy Caution, Slim Callaghan, Perry Mason, Hercule Poirot etc. etc. I was maybe nine years old at the time, and for most kids it was perhaps Superman, The Hulk or even The Beano held sway?
The educational limits of that local school exhausted, I was then shoved into a boarding school far away, run by American, Canadian, Australian and Kiwi missionaries. If the 'morality' of those people is reflected, today, in the mindset of the religious groupings in the States, God help the world. Has anyone imagined fundamental extremism to be peculiar to the Middle East, they are sadly, and most dangerously, mistaken. Those years in the latter establishment were the most unhappy and spiritually crippling of my life. I am surprised that I found the inner strength to rise above the experience and discover a private faith, any faith, of my own. In my mind, none of the established religions represents anything much more than degrees of power lust and the desire to exert mind control for a plethora of different, possibly unhealthy reasons. I think that, in truth, God is seriously misrepresented by most of these groups. That they may, however, have some positive spin-off consequences is a saving grace.
Whether there is a general acceptance of what may be a "standard issue" of morality perception is, well, difficult to say: one would have to know, intimately, far more people than I do in order to form an educated guess. FWIW, I suspect that people do, by and large, accept the morality behind the Sacred Ten, whether they actually do or do not live by those codes being something entirely else. Of course, that does mean that one has to exclude all extremists from any consensus of opinion or it will be distorted too far to make a broad, general sense of where we are today.
Rob C