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.
Some characters would be happy. If the fanfiction portrays them in a positive light, for instance, highlighting their best qualities or giving them a happy ending that they didn't have in the original anime, they would be glad to see it.
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.
Some characters might be amused. They could find the different interpretations in the fanfiction entertaining and might even share it with other characters.
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.
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.
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?'.
A few might be angry. If the fanfiction shows them in a negative light or changes their backstory in a way they don't like, they could get really mad. For example, if a character with a noble past is made into a villain in the fanfiction, they'd be furious.
Some characters might be angry if the fanfic misrepresents them completely. For instance, if a heroic character is made into a villain in the fanfic, they would surely not be happy about it.
Some characters might be critical. Elsa, being a powerful and responsible character, might not like it if the fanfiction misrepresents her in a way that goes against her values. She might think that the writers should be more respectful of her character arc and not make her do things that are completely out of character just for the sake of a wild story. However, at the same time, she might also appreciate the creativity in some parts.
Some would be intrigued. Captain America, being an open - minded person, might be interested in seeing different interpretations of their team dynamics. He could even gain new insights about his relationships with his fellow Avengers through the fanfiction.
Some Avengers might be really confused at first. For example, Tony Stark would probably be intrigued yet find it a bit odd. He'd be analyzing it like he does with new tech, trying to understand the appeal and the different universes within the anime fanfiction.