I think you just have to be completely honest as to who Jonah Hex is as a character. There is a temptation to make him be seem more honorable than he probably would be in real life. He is a Bounty Hunter, I don't expect him to be a champion for human life.
It's nice to say he probably fought for the confederacy out of necessity or bad luck or whatever, but it's probably just as realistic to think he wore that costume with full understanding of what it meant. You have to just say to to yourself, how realistic do you want the character to be and what does that really mean.
When I watched Cowboy movies as a kid, the villains would be "Indians." I knew who the heroes were supposed to be and what I looked like and they weren't the same. I am a Jonah Hex fan but I accept that Jonah is probably just as much villain as hero. In the V for Vendetta books, there is a hero called Strom Saxon, Jonah Hex reminds me of that. So does the Minute Men documentary on the Watchmen TV series. I say change the costume, retire the character, or accept that he is kind of a villain.