Cardinal Newman in his letter to the Duke of Norfolk after the declaration of papal infallibility was very careful to distinguish the true voice of conscience from subjective ideas. When men advocate the rights of conscience, they often don't mean the rights of the Creator, he says, but of their judgment and humor without thought of God. Conscience has rights because it has duties. Conscience doesn't have a right to dispense with conscience. It is not the right of self-will.
Conscience has to be rooted in truth.
Newman rejected the liberal frame of mind which has no need for truth. Conscience is the voice of God in the heart of man, distinguished from the voice of God in revelation. There is a principle planted within us before there is any training, though training is important to the proper reception of the principles. Newman attributes to the conscience all of the attributes of the papacy except infallibility. We don't have the same objective certitude as papal declarations.