Me, I go for inclusive, while wrestling, mostly inside my own head, with questions like "Why isn't Obi Wan Kenobi a magical negro?" or, to put it another way, is it racism if I make Obi Wan Kenobi black?
(Having been told I was guilty of stereotyping when a gay character dies at the end of Scardown, it's now the sort of thing I think of a lot. No mention was made of the two bisexual characters who survived....) (I also killed off some black and Asian characters. And a whole BUNCH of straight white people. Is it racism if I make sure the brother always makes it out alive?)
I think the guilty tic, the offensive thing, is othering. If women or gays or blacks or Asians or whites or men or whatever are representative of the mysterious inhuman, either through idealization or denigration, if they are unpersoned, then you have a problem on your hands.
Bad writing, unfortunately, does not qualify as cultural appropriation. Otherwise, I'd be standing on my heritage as a Slav to excoriate some authors of vampire fiction.
mrissa makes a very good point: it's also an issue to lump Europeans together in one group or culture. I'm mostly Ukrainian and Swedish. We historically suck at oppressing people, being mostly concerned with hiding enough food from the Russians and Finns to make it through the winter.
yhlee has a good point when she says it runs the other way--that there are expectations upon her writing because she has an Asian name. That there is the expectation, in other words, that her work will be--dare I say it--ineluctably non-Occidental.
I'm not Australian, but if I need to write about a bunyip, I will. And have. And I will grant that tradition exactly the same respect that I grant the Christian tradition, or the Celtic one, or.... (yeah, those are big hunks of pie I'm hacking off there. Just run with it.)
...which is to say, I'll pick it apart to see what makes it tick, and build cool things from the clockwork bits, as truepenny said. I've heard it said that 'Europeans' should only approach the cultural treasures and stories of others with due respect and a hesitant step, and only if invited.
But I can't grant the story bits undue respect. There are things I would not write down, ever, because they are things that are not written down, and I respect that. There are places I would not go, unless invited. I don't mock in other people's churches. (And everybody's church is somebody else's church to me: I do not belong to any religious tradition.)
But stories are my culture. They are my only culture. They are the country where I live. I get help, when I don't know them well, and try to find people who can help me make them work.
But I refuse to live in a country that is only inhabited by white Americans.