Personally, I generally don't like fanfiction where it changes the characters in the story. If the people who read it and write is believe that it is gospel and that the actual canon story is nothing but a not on the side of the road, then they're crazy. I honestly don't understand these people. I've read a few fanfiction with canon characters and they were okay, but nothing to write home about. I do know there are gems out there but I haven't found them yet. Even still, I am utterly confused as to why they believe it is the truth but hey, who cares anyway?
However, fanfiction which uses OCs (good ones, not the crappy overused ones) I can mostly get behind. I'll admit that I'm trying to write one right now, although it's for RWBY not Fire Emblem, so that might be affecting my opinion. Anyway, unless your characters are the pure embodiment of absolute shit, I'm fine with it. Again, don't treat it like it is the Bible.
What I'm trying to say here is: I'm fine with fanfiction as long as people who write and read it don't treat it as more canon than the actual story.