Once upon a time, in the heyday of radical protest known as the 1970s, Marlon Brando turned down his Academy Award. It was for his 1973 performance in The Godfather, and his refusal had nothing to do with the film, his portrayal of Vito Corleone, or the Oscars in general. It had everything to do with the treatment of Native Americans.
You know the story, of course. The clip of Sacheen Littlefeather, dressed in full Apache clothing and declaring that Brando refused the Oscar due to "poor treatment of Native Americans in the film industry" gets trotted out at every Academy Award ceremony with a bit of an eye roll. Remember those crazy days, Hollywood asks itself, those days when streakers ran by and Bo Derek wore a poncho to present? Wasn't it rather appalling, really? Isn't it grand we take it so seriously now, as they did in the Golden Days? (Hint: they didn't, at least if the likes of Jimmy "it was just a big party" Stewart are to be believed.)
Now that the Oscars are such grave business -- and one might argue that they clearly were even in 1973 if Brando felt rejecting one made a big statement -- will we ever see an actor, actress, director, or screenwriter reject one again?
I suspect we won't, for the simple reason that it would be career suicide, especially if it was done for a political reason. We now live in an era when the most bland political statements are blown wildly out of proportion. I find it rather inexplicable, really. Surely in a land of free speech we can respect the opinion of Johnny Depp and Alec Baldwin as ... well, just that. An opinion. If an actor or actress rejected their Oscar on the basis of any cause, no matter how sympathetic and cuddly, could the reaction be less than catastrophic? The industry would reject them for being so cold and callous toward this, The Biggest Creative Award Ever, and audiences would reject them because they ceased entertaining, and started opinionating, even if it was something as inoffensive as "Stop puppy mills!" This would then loop right back into their field rejecting them, because while they may have privately applauded their stance, they won't back them if they're not viable at the box office.
I should probably add that a screenwriter, composer, or even director could probably stage a political rejection and escape relatively unscathed in audience estimation because they aren't the face of a film. There are exceptions -- Steven Spielberg, Martin Scorsese -- but for the most part, a Tom Hooper is forgotten the moment he wins. Naturally, this doesn't apply to the industry itself, but if the money and acclaim roll in, I suspect the faceless artist could continue to work if their statement wasn't too horrific and controversial.
The only reason I could see an Oscar refusal being "acceptable" would be if it was done for creative reasons. If it was painfully and hideously clear that one of their competitors deserved the award more -- say, a Tom Cruise won over a Daniel Day-Lewis -- and they pulled a Ving Rhames and gave it away (not that Rhames didn't deserve his Golden Globe -- let me stress that!), then I could see it being applauded as a gracious and delightful gesture. There might be some frowns and distancing, but it wouldn't last long, unless the whole thing was just seen as embarrassing and crazy. (Katherine Heigl's pointed "I refuse to even be considered for an Emmy nomination" is a good example of how a refusal of a statuette could be seen as poor form.)
But finally, I don't think we'll ever see an Oscar refusal because those in question want them too darn much. I once spoke to an Oscar-winning director who freely admitted it was the ultimate prize and that everyone wanted one, regardless of how much they insisted they didn't. (That's not to belittle anyone. We all want recognition and prizes, no matter how pure our art.) There are other ways to make a statement, and when you work that hard to get that golden statuette, there's no way anyone is going to toss it away for a bit of dramatic airtime, or because they feel undeserving of it. No one truly believes they didn't put the effort in.
Besides, can anyone really follow up Brando and Littlefeather? That was a one-time deal, and to mimic it would be exactly that. Someone who cares deeply about some plight or creative slight will have to find another way, or risk the eye rolls that would result.