Not all characters would enjoy it. Those who are very set in their ways or who have a strict view of their own story might not like the deviations in fanfiction. But there could also be characters who are flattered by the attention they get in fanfictions. For example, some minor yokai characters who don't get much attention in the original might be happy to see themselves as the center of attention in a fan - written story.
It depends on the character. A proud yokai might not like a fanfiction that portrays yokai in a negative light or inaccurately. On the other hand, a more open - minded character could enjoy seeing all the different interpretations. For instance, Shigure might be more likely to enjoy various fanfictions as he seems to be a bit more easy - going and interested in new things. He might find the creativity of the fans quite refreshing.