I don't believe that "Gut Feeling" is exclusively highly developed among persons without a formal education in science. There are many examples of self-educated persons who have a highly developed sense of direction that is not consciously derived. In fact, I think a person educated in science, who is also a free thinker, will have an even higher developed and more sharpened "Gut Feeling". The label may be the more eloquent "Intuition" or "ESP".
In the same way that you may describe an uneducated person as having been "Conditioned" by authorities in family and religious leaders, an educated person can likewise have their subconscious reasoning powers "Buried" under "Conditioning" by authorities in their "Secular" education. Exposure to a greater range of original ideas can hone and actually enhance intuition and "Magical thinking" that springs from the incredibly powerful unconscious mind. Yes, this honing can occur IF one preserves one's independence of thought and a healthy skepticism.
However, we have seen.. I have seen.. highly educated individuals who are so thoroughly indoctrinated and bound in the ideas of others who are "Experts" or otherwise authorities in their field, that they have few original ideas or positions of their own. Perhaps a better perspective would be to say that DOGMA, whether within or without exposure to a science-based "Education", confines the mind and limits development of the higher functions, including an amazing, uncanny intuition or "Gut Feeling".
The concept of the "Renaissance Man" perhaps expresses the ideal of leaving behind dogmatic ideas and freely exploring BOTH in realm of Human Nature and in Physical Nature. However, there is no escaping the Human Nature proclivity for ego, power, and control over others by the promotion of a limited set of ideas to the exclusion of others. This manipulation occurs not just in the experience of the "Uneducated", but also in every field of study by the power of political and religious intolerance.
Pure science in the study of Human Nature, or in the study of physical nature, is rarely performed devoid of self-interested perversion by Human Nature itself. The politics of science can be as severe as the politics of religion. Science in Physical Nature produces verifiable truth. The science of Human Nature can also provide verifiable truth, and that is what we are looking for here.
One of those verifiable truths in Human Nature is that we seem to have a need to believe in a superior intelligence, whether it be a deity, or the laws of physical nature. Unfortunately, these two exclusive ideas are blended in religion. They should never be blended or melded. Diety resides entirely in Human Nature - "The Mind", and Physical Nature resides entirely within its own "Laws".
Yet, when it comes to accurate "Gut Feelings" or "Intuition", it is strong evidence that the ultimate higher power is WITHIN US. This higher power is best described as our own subconscious mind that is powerful beyond comprehension.
If God is the superior intelligence we all seek to know, then each one of us can know God by feeling, growing, and better using our subconscious mind. We can then become ONE with God, the all-powerful, the all-knowing, to achieve the ultimate objective of religion, and the ultimate secular experience as well.
Organized utopian social structures pretend to facilitate understanding the human experience we call life. Those that are INTOLERANT of alternative ideas will want to manipulate us. This pulls us away from independent thinking to conformity, and away from the very personal "God" experience. If there is an apt description of the Devil, it is intolerance and manipulation. If there is an apt description of God, it is our own individual, independent, all powerful, all knowing subconscious mind.