This is, of course, a matter of personal opinion. The degree to which you think that religious people are guided by a “still, small voice” depends a great deal on what you think of religious people and their level of sincerity. My own view is that not all religious people are the same. Many different people can claim to base their moral decisions on religious authority or guidance, but not all are truly listening to a “still, small, voice.”
The story of the still, small voice in I Kings 19 can be interpreted in many ways. One way to look at it is to say that God really speaks to us quietly. His word does not come through the bombast of the great wind or of the earthquake. What God really says to us comes in the silence and it is something we have to strain to hear.
It is not clear to me that all people who claim to be guided by religious authority are really listening to the still, small voice. I think that if more people were listening to that voice, there would be less religious certainty and people would be less judgmental. I think that many people who claim to rely on religious authority are really listening to the wind and the earthquake and are actually speaking themselves in those same ways. They are not listening to the subtlety of what God is trying to tell them.
Of course, there are many religious people who do listen to the still, small voice when they make their moral decisions. I think they get drowned out by the people who do not listen to that voice. So my take on this is that you cannot prove that you are listening to that voice simply by saying that you base your moral decisions on religious authority. The proof is more in the substance of what decisions you make and how you communicate them to others.