So, question to everyone here who objects to fanfiction: Does your arguments also apply to other types of fanwork?
My objection to fanfiction is based solely on the butchering of the character's personalities. If the fanfiction doesn't use those characters, or uses them only as supporting characters, or in some cases makes a genuine and successful effort to get those characters right, then I've no problem with it. But just using somebody else's characters, you're likely to misunderstand their motivations and their experiences and create characters who are caricatures of the originals. I think that can be bad for the fanfiction writer and bad for the original author. Those things are less likely to happen with artwork, and I can respect that a lot more.
Then of course there's the slasher stuff.