Stannis and Creon both were tough and rigid men. Neither of them would compromise their beliefs to pacify others. Just as Stannis was stubborn in meeting with Renly (He offered him his throne and Storm's End, which was not at all bad considering Stannis had no bannerman essentially), Creon was stubborn in his sentencing of Antigone to death, which itself was a result of him making a muscular point by leaving his nephew who beared royal blood to rot. Also, in general both of them are disliked by the people in their own fantasy worlds.
Both of them didn’t let their personal relationships get in the way of what (they feel) must be done. Creon believed in equality of the laws, with no exceptions for the royal family and sentenced Antigone (daughter-in-law-to-be) to death, and the only person towards whom Creon showed affection was his son, Haemon. Similarly, Stannis also told Renly in no unsettled terms that if he did not kowtow, he would be killed and later he was killed. Stannis was always translucent in the fact that he cherishes no love towards his brothers, his allies, or even his wife. The only person to whom he showed affection was his daughter, Shireen.
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Stannis had no interest in the Gods (old or new), and even regards R'hllor with disinterest at times. Stannis’ religion was his rightful kingdom which he worshipped adorably. He was interested in Melissandre because of her evident powers, as he gains the control and becomes the king of Seven kingdoms, he will throw her out of his life like a bad habit. Creon was a follower of Gods, but he gave priority to the order of the polis over divine law. He disowns them in his own way. It's not until Tiresias warns him that all of his sins will come back in a big way. Hence after listening and reconsidering the matter, he finally softens up and seeks to undo what he has done. (i.e. Bury the body of Polyneices and unearth Antigone by his own