The Watcher
Judging you from afar
You don't think he has done enough of that with the one true king of Westeros already though?
So far in the show - Stannis is portrayed as an opportunistic, religious fanatic that is willing to do just about anything to win - including burning his own daughter. They literally don't have time to delve into the nuanced reasoning behind it, so it comes across as bad all the time. Even the Stannis scenes that show him in a good light don't do enough to show any kind of character development.
So far in the books - Stannis is so far portrayed as the rightful king that has gotten shyt on by everyone his entire life, even though he did all the heavy lifting for them to succeed. He doesn't burn people at the drop of a hat, instead he tells them to pray harder. He talks about how much he loves his daughter who is his only heir. He went along with killing Renly, but it's arguable that he was somewhat justified in that action. He figured out the Lannisters were putting their incest babies on the throne before anyone else got around to it. He's been shown over and over again to be a fair, just person. Davos respects him and Davos is the greatest.
I think as of last night, the show has jumped way ahead of the books. I think they sped up the Stannis storyline because there are only 2 seasons left and what we saw is going to be similar to what GRRM eventually does, show how a man who is the best fit to rule and actually cares about the threat of the Others getting corrupted by ambition and prophecy. That is on level with what he's done with every other big character so far in the story. It's Macbeth.
Don't get me wrong, I like the Stannis character quite a bit. He may well end up saving the entire world in some way. Maybe burning Shireen does something that we don't know about yet that will change the game. Maybe he is actually Azor Ahai and was right all along.
But I do believe whatever happens, GRRM told the show runners about it already and they are writing with the end-game in mind, so all these people freaking out about how the show is ruining the characterization of Stannis are forgetting that we don't have the complete story yet and there's still a couple thousand pages that could easily turn Stannis into a man that would burn his own daughter for some greater good reason.