St. Thomas Aquinas, the greatest theologian in Church history, clearly taught the supremacy of conscience against those who would impose a religion on a non-believer. The most profound exposition on the topic was given by Cardinal Newman. The Catechism quotes a key passage by him:
"Conscience is a law of the mind; yet Christians would not grant that it is nothing more; I mean that it was not a dictate, nor conveyed the notion of responsibility, of duty, of a threat and a promise. Conscience is a messenger of him, who, both in nature and in grace, speaks to us behind a veil and teaches and rules us by his representatives. Conscience is the aboriginal Vicar of Christ."
As the "aboriginal Vicar of Christ" the human conscience obviously has certain rights. But as Newman points out: "The conscience has rights because it has responsibilities." That sentence is the theme of Pope John Paul's encyclical: Veritatis Splendor, a rigorous defense of the moral law found in every human heart.
So what is the problem? While everything necessary to guide us can be found in that inner chamber, it is often obscured by external manipulation. (Some of the slogans I am analyzing here are attempts to do that.) We all like to consider ourselves above such influence or that only the "simple minded" can be easily manipulated. Just the opposite is the case. Consider: Hitler's strongest support came university students and professors. Intellectuals are peculiarly malleable when it comes to throwing the moral law (conscience) overboard.
Our greatest defense against manipulation is what is called "conscience formation." The classical approach to forming conscience was developed by the ancient Greeks. They considered that we already know right from wrong. We are born with that knowledge. At best we need to be reminded. However, we fail to act on what we know because of our emotions, our passions. Conscience formation is really cultivating emotions to go along with what we know is right. For example, during a battle a soldier knows he must stand and defend his fellows, but his emotion of fear tells him to run. Then he sees the flag and all the emotions he has associated with home, family, country sweep over him and move him to hold his ground. He has developed emotions which enable him to act heroically.
Even today the challenge is not so much hammering young people with "Do this" and "Don't do that." By and large they already know, but need help with their emotions. As Pope John Paul noted, young people everywhere, boys as well as girls want a "beautiful love." That is, a love that is pure, that expresses a total self-giving. But the emotions, the passions mess up that ideal. We need to help them develop the emotions to go along with their deepest longings. The Greeks did that by stories and poetry, for example Odysseus returning to his beloved wife, Penelope. A contemporary effort to do the same is William Bennett's "Moral Compass," a wonderful collection of stories to aid parents and teachers in developing good emotions in the young.
We do have a greater challenge than the Greeks because our emotions have become so alienated from our sense of right and wrong. A disgruntled professor of moral theology summed up the modern dilemma this way: "It is now OK to have sex with any consenting adult—so long as you don't smoke a cigarette while you are doing it." The problem is really that we have developed strong emotions around certain questions like smoking, drinking and driving, killing animals for their fur, but very weak ones about other matters such as taking the life of an unborn child. I remember once listening to a women calling for the strictest possible sanctions ("zero tolerance") against those who drive after drinking alcohol, and at the same time arguing for choice when it came to ending a pre-born child's life. It was not that she did not believe abortion is wrong. She knows the fetus is a living person; she just does not have any strong emotional response to "it" (not even really a him or her).
For more on the problem of conscience formation, I refer you to C.S. Lewis "The Abolition of Man." He considered that his most important work. I especially recommend the section "Men without Chests" which analyzes the dilemma presented above.