You have a greater responsibility to your audience when you write fanfic than when you write original fic because you're dealing with characters that are already REAL to so many of us.
I agree that death, rape, or serious and upsetting issues should have warnings, but for me, it's not because it's fan fic or the characters are "real." I believe that all characters should be real to the readers or their author has failed. To me, it has nothing to do with fan fiction.
With original fiction, as others have pointed out, there are summaries on the backs of books, reviews, the notes in the publisher's catalog, and a million other ways we know what we're "in for." I would never pick up a book not knowing what it was about, and I do not read stories in which animals or children die or are abused, and virtually never read stories about death, rape, war, torture, suspense, horror, or other forms of violence and suffering. I don't want to. It's a fiction rule and has nothing to do with fan fiction specifically.