Well, there are also those characters who might be a bit shocked or confused. Take Levi from Attack on Titan. He's a very serious and no - nonsense type of character. If he were to read some of the fanfic about him that deviated too much from his own self - perception, like being made into a comical or overly emotional character in the fanfic, he might be taken aback at first. But then he might also realize it's just a different interpretation and not take it too seriously.
Aang might go into a deep state of depression. He has always been an emotional character, and having his heart broken by Katara, someone he loves deeply, could send him into a downward spiral. He might isolate himself from his friends and stop practicing his bending for a while.
Katara would likely be shocked and initially angry. She has feelings for Aang and would be hurt by this unexpected turn of events. Zuko, on the other hand, might be conflicted. He wants his sister to be better but this situation is so out of the ordinary. Toph would probably be more straightforward and say what she thinks, which could be a mix of disbelief and amusement.
Well, it depends on the nature of the fanfiction. Some anime characters might be amused if the fanfiction is light - hearted and full of comical situations. For example, if it's a fanfic about a cooking competition among the characters from a shonen anime, they might react with good - natured laughter and competitiveness. They could also be confused if the fanfiction takes their story in a very strange or unexpected direction, like suddenly making a character from a historical anime end up in a space adventure.
Katara could be heartbroken. She might initially be in denial, not believing that Aang has actually left. Then she could become angry, feeling betrayed by Aang's sudden departure.
Kakashi would be very observant. He would look for how the fanfiction writers understand the world of Naruto, the values and the moral lessons. He might even use some of the creative ideas from the fanfiction in his own teachings if he thought they were valuable and in line with the spirit of the original story.
There could be characters who are outraged. If the fanfiction distorts their personality or makes them do things completely against their nature, they may be very angry. For example, a noble character made to act like a coward in the fanfiction would likely not take it well.
They might be confused at first. RWBY has its own unique lore and concepts that are different from many anime. So anime characters may need time to understand things like Grimm and Huntsmen. For example, if Goku from Dragon Ball was watching, he'd probably be like 'What are these strange monsters?'.
They could be surprised. The fanfiction might show them in scenarios they never imagined, like a shy character being in a very bold and adventurous situation.
The Fire Nation, which has now become more of an ally, would also see this as a positive thing. Zuko, being Aang's friend, would be happy for them. He would see it as a sign of peace and unity among the different nations. The Fire Nation people might send some precious gifts as a sign of their respect for the union, as they know how important the Avatar and Katara are to the new world order.