This is an issue that is pretty complicated.
You know when you read a fanfiction about a canon character, and the writer has their personality wrong? When the character does and says things that they wouldn't do? Frustrating, right?
Yes. But it's harder than that.
Everyone has a different view of a character's personality. For example, I see Hollyleaf as a hypocritical, obsessive murderer who got off the hook. However others see her as brave and loyal.
I wrote this sometime last year, and I can say, my opinion has definitely changed. I don't view Hollyleaf as a hero. I don't particularly like her, but I view her instead as a morally grey character who had a LOT of potential. Specifically antihero potential. This is a good place to state that it's important to analyze characters and form an opinion based on actual thought, rather than just following the "cool" opinion. This can be difficult in a fandom where one opinion is seen as a correct opinion, which is very toxic. Of course, some people do it just for fun and don't want to analyze. That's okay too, but IG you're going to be serious, I recommend understanding more about a character. Learn their motives, their mistakes, and their good deeds. Try to develop them more than the Hunter's did, because their characterization is severely lacking. You are still able to hate a character while understanding them.
(Update added 27.11.17 - 4.46 am. Time to sleep, I'd say.)
How is there such a difference?
Interpretation is difficult. And personalities are no different. So is there really a correct way to write them?
Yes. There is.
Most characters can be narrowed down. To their traits, to how they would think, how they would say. They need to be properly analyzed.
For example, say you were writing about Yellowfang. Cinderpaw/pelt would most likely make an appearance. It doesn't matter if you dislike Cinderpelt, she would never snap at someone without a reason to. She would never knock over a kit, for example.
Say you were writing about Scourge. Scourge isn't some tragic victim who can be tamed by a she-cat. No matter his past, it doesn't excuse his actions, Scourge is a relentless murderer, he doesn't care about other cats. Scourge is possibly incapable, or simply doesn't care, of showing love to another cat. And even if he did, this she-cat wouldn't miraculously change him into some precious, loving little angel.
Or what about a Firestar fic. It doesn't matter if you hate Sandstorm, she wouldn't just yell and Firestar and constantly be offended and angry. She does seem to be offended easily, but know she has mellowed out.
As you can see, reading a fix with character's that act completely uncharacteristically is so aggravating.
So, If you are writing about canon characters, try and portray them they way they were in the books. You can't please everyone, but if you do write wrong, then people will not read your stories.
Really, whenever I read a fanfiction with a canon character acting like they usually wouldn't, it makes me want to pull my hair out.
Analyze your characters. Write them right.