I've got a very complicated response to this, but I'm going to read the article that Liam has posted to (I've only read responses to Shriver's speech).
On a personal note, as somebody who writes short stories for fun (I've got a long way to go before I've got something that can be published), I can say that I've struggled with this idea of appropriation and where, exactly, the line is drawn between that and appreciation. I've come to the conclusion that, at least for now, I don't understand other cultures well enough to write from within those perspectives. I've tried and it just doesn't sound real or honest, and I feel like it is how I imagine people from other experiences feel rather than how I understand them to feel. Does that make sense? To my mind, it requires an immense amount of writing and insightful maturity to pull it off, and a helluvalot of communication and connection with and knowledge of whoever it is you are trying to write about.
Part of this comes down to historical relationships of power and oppression and how groups have been represented in literature in the past (and present) in ways that strip them of agency and good, honest representation.
That said, as a person who is interested in race and culture and gender and all sorts of other things that are mostly unrelated to my experience, I've decided that, at least for now, I can write about them but as an outsider - where the narrator or protagonist is looking out from their privelege and trying to make sense of the world around them, one which is very different than the one that they grew up in and which doesn't conform to their perception of reality. Does that make sense?
For what it is worth, I think that William T. Vollmann does this quite well - it is a good balance, even if it is, at times, concerning in some of its depictions and characters. His goal, though, always seems to be humanizing people, recognizing their inherent sophistication and beauty even when they do at times conform to certain stereotypes, which is something beautiful and important in literature as far as I'm concerned.