At the risk of beating a dead horse, here's her insurmountable problem: for every one person who thinks everything she does just shows how "real" and "authentic" and "non-Hollywood" she is, there are massive truck loads more people who look at that same behavior and think that it is entitled, spoiled, self-absorbed, immature, unintelligent, you name it. No amount of persuasion will convince the people who can't stand her to suddenly like her, and vice versa. The facts are that she is extremely unliked by the vast majority of the public, and that will not change no matter what any one of us says. Career wise, that's extremely difficult for an actress to overcome.
Personally, and this may be pure opinion on my part, I'm quite sure most people started disliking far earlier than the cheating scandal but tended to make excuses for her because the Summit-paid media was making excuses for her. The cheating scandal was the big reveal. Forget Rpattz - the public felt played, duped, betrayed by the persona that they were being force fed. And it's trite but true that once you betray someone it's damn near impossible to earn back that trust. She hasn't done anything to earn back the public's trust. So maybe on some level this public animosity towards her does stem from moral grounds - it's just not the sexual mores you're thinking of.
