It is important to make a distinction in between a flawed hero and one that cant be forgiven at all. Readers will forgive pretty much everything, given the right circumstance. But not these things. Unless you want your character to be crazy unlikeable, these are things that you should avoid if there is any hope of your Hero staying that way.
Number One: Child Abuse
Example: Lolita and Anakin Skywalkers killing the younglings in Star Wars.
Children are meant to be protected and in most people abuse to children will trigger a protective response. There is a reason why even in the real world child abusers and pedophiles often have to be separated from the general population. This goes for child rape, physical abuse to children and the common “Making an orphan” trope such as the Bride in Kill Bill.
Not everyone likes children and your hero certainly doesn’t have to. I have a character who I love who is literally afraid to be around children because she worries about turning them into her. However, not liking children is totally different from child abuse, sexual abuse or killing a child
Number Two: Animal Abuse
Example: Moises in Desierto
Even while being hunted by the racist Jeffery Dean Morgans character Sam, Moises made me stop rooting for him when he violently blew up Sams dog Tracker. He might have been the hero but you can’t kill the dog! Animals are trusting for the most part and killing a domesticated animal is one of the more vile things anyone can do. I can watch JDM bash in someones face with a baseball bat but if you kill a god or I see a dying, animal it’s pretty much over.
It will kill your reader’s interest pretty damn quick. If you must do it make sure to do it at the very end of your story like Ol’ Yeller or Where the Red Fern Grows.
Number Three: Selling out of Your “Kind”
Example: Jake Sully in Avatar
If they are your adopted kind that is even worse, as in Avatar. As a hero I expect you to have character development and selling out will make me dislike you faster then you can say flying dragon birds. After all of the time and investment that your readership has invested in the transformation and the development in between your hero and the society they are in, they are going to feel just as betrayed. There is very little organic transformation that your character can take to find a road to forgiveness and if there is….its probably going to take longer then you have.
Number Four: War Crimes
Example: Benjamin Martins War Crimes- The Patriot
Fiction meeting fact can be a dangerous thing when actually educated people find out about it. There has been criticism by people that Ben Martin, played by Mel Gibson (which we will not get into), is actually based on Francis Marion, a militia leader in South Carolina known as the “Swamp Fox”. He has been said to be a serial Rapist and a man who hunted Indians for fun, committing crimes just as bad and sometimes worse than the British military during the Revolutionary War.
Away from the idea that this character was based off of a real-life rapist, Martins Character himself’s main struggle was dealing with guilt over Torture, mutilation and atrocities he committed during the French Indian War.