Is it fair to assert that those who use religious guidance or authority as a basis for moral decision listen/conform to a "still, small voice"?
This is a pretty weak metaphor for how a person “knows” or “believes” his/her moral decision is based on some universal “guide” who “speaks” to us if we listen closely. There is a psychological impulse that directs our action based on what we have learned about human behavior from our past experiences, including the “teachings” of our superiors (elders, church leaders, parents, teachers, etc.), and if we want to refer to this impulse as a “voice”, that’s fine, but it is a delusion to think that some higher being actually speaks to us in some language. The study of how we “know” things is called epistemology; one way is by subconscious structures of “rightness,” unarticulated and unarranged by “logic” but formed by our lives to date.
Morality is subjective and is conditioned upon the circumstances one preaches / follows the morals in. Some of them are generally valued by nearly all cultures/religions such as honesty, helpfulness and so on. The reasons are not elaborated in this answer but, certainly, there are very pertinent ones.
One using 'religious guidance' as a basis for a moral decision cannot be always ruled out as listening to a 'still, small voice' by another with mere intellectual reasoning. Sometimes, and especially when the guidance is used on one's own way of life, the adherent has experiential knowledge which is seldom felt/sensed by the others. This knowledge is by no means a 'still, small voice'.
However, to call these guides as 'authorities' is taking things too far as, in that case, the adherent would fail to apply circumstantial reasoning. The adherents can be ruled out if the moral values referred are found to be detrimental to the benefit of mankind's mental/emotional/spiritual uplift or causes pain in any form to others.