In the subtitle to this post, I speak mostly of H. P. Lovecraft, whose views on Jews and other minorities was complex at best, hateful at worst. There are elements of his stories that I may cringe at, in the way that people cringe today at yesterday's racism, sexism, et ceterism. But I never worry about buying a Lovecraft book or seeing a Lovecraft-inspired movie because Lovecraft is very, very dead--he's long given up the fight against blacks and Jews, so if I give money, it's not going to come back at me in the form of anti-Semitic commercials and laws.
But let's take the case of Orson Scott Card, whose Ender's Game is finally being made into a movie. Let's say you like this book (I don't) and want to go see the movie, but are turned off by Card's political views, which seems to be the situation that Alyssa Rosenberg is in. (If you hadn't heard, Card's anti-gay opinions stretch as far as contemplating revolution against a government that endorsed marriage equality.)
Here's the decision tree I've worked out. If you answer "Yes," at any time, stop; but if you answer "No," go to the next question:
A) Does the work in question endorse the political view you disagree with vehemently? If yes, then skip it. (Though we should note that there's room for debate, there may not be room for propaganda in this. So you might go see a movie which included homophobia; but not a movie that endorsed it.)
B) Does my consumption materially support an opposing political view? Which is a complex question, so I'll break it down:
1) Does the creator (or creators) work towards this political view or contribute towards this?
2) Does the creator (or creators) benefit from my consumption?
As it turns out, this is a very short decision tree. Let's see how it works in practice for Ender's Game the movie and Card's homophobia:
A) I don't think Ender's Game is homophobic, so go on to question B.
B1) Orson Scott Card definitely works against LGBT equality: he's on the NOM board at least. He probably also financially supports such groups, though that's less clear.
B2) This is a harder question to answer. First, I don't know if Card's contract gives him a percentage of the movie profits. And I also don't know if an Ender's Game success will inspire people to option other Card novels and make them into movies: I don't see a Speaker for the Dead movie or some Alvin Maker movies, but I suppose it could happen. Because Card works against gay rights, this question requires more research (does he profit from this movie?) and speculation (will a success here lead to profit from other movies?).
So if Card stands to make money that he might use against (not to put to fine a point on it) my sister, then I might skip this movie even if I were interested in it.