Stannis didn't just kill Renly, he murdered the Storm's End castellan (who wanted to have an honest duel iirc) and he also presented the argument that would defend the burning of Shireen when talking about Edric Storm.
We all want him to be the man Davos thinks he is, but Melisandre has obviously been corrupting him, and each time he fails she gets inside his head more. That's what D&D meant when they said his arc was always leading up to this from their introduction in the show - she manipulates him more and more and when he's a completely broken men she gets all the way through. Of course episode 9 failed to convince us he was broken but it was obvious that was the intention.
He's not a religious person, he doesn't believe the red god, but he believes in her magic and he definitely really wants to sit the throne. That's his entire purpose for going north. To save the realm is what everyone gets from the cart-before-horse quote, but what it really says is that he's doing all this shit because he wants the throne.
