To examine the situation more closely, we should have a terse discussion on what death of the author is. Death of the author is when a creator's intentions are null and void in interpreting their work. This is often invoked so that way people aren't left thinking there's only one correct interpretation for a piece of work, such as a book or a movie, and thus discord is sown amongst fan bases. Now death of the author gets a relatively bad name these days, and that's largely cuz stupid people invoke the term so they can continue consuming media that was created by terrible people and evade any sort of guilt. That's not how death of the author works. If you're still consuming the media of an awful person because you just don't give a fuck about what they've done since it hadn't effected you personally, that is not death of the author. For example, you can't claim death of the author in any of the songs on Megadeth's Endgame because Dave Mustaine himself said that the songs are directly based on his political views (which if you know them, are pretty fucking obnoxious). You can still enjoy the musicianship, but you can't say that Mustaine's beliefs aren't present in his music. On the flipside, you can do this with Aerosmith since none of their songs involve impregnating a teenager and then convincing her to get an abortion (but still, fuck you Steven Tyler).
But that leads into the next question: is death of the author a good idea from a moral standpoint? This is where things get tricky. Obviously if you find out the creator of your favourite book/movie/game series is a scumbag, you'll want to justify your fanship somehow, because their creation happens to be really good and/or might have shaped you in some way. Lovecraft fans can talk with you for hours about that. And trust me, there's a solid 50% chance your fave is problematic. You could just take the easy way out and be like "well as long as their beliefs aren't present in their work then I can still enjoy it", but that won't be as easy as you think. Because you see, a creator doesn't have to be overt in blending their personal philosophies with their work. Frank Miller's 300 almost romanticises ancient Sparta, which was a eugenic military dictatorship that reveled in slavery, and portrays the Persian kingdom, who in all actuality were very progressive and egalitarian for their time, as the arseholes. Now Miller doesn't openly announce that he's in favour of slavery, military dictatorships, and eugenics, but the fact that he portrayed a civilisation that exuded such qualities as heroic and likable is pretty damning that he likely doesn't find them too deplorable. So how does this relate to J.K. Rowling you might be asking? Well I never read any Harry Potter books, but I have plenty of friends who have, and many recent internet posts have been pointing out some of Rowling's other subtle prejudices, such as making the bankers long nosed goblins (I'm sure I don't have to tell you who that's supposed to symbolise), naming Dobby, an elf who only wears tattered clothing, after the word dhobi, which refers to the poorest in the Indian caste system, and naming the only prominent Asian character Cho Chang, like for real she might as well have named her fucking Pork Fried Rice or something. So Rowling, aside from being transphobic, also might have a racism/classism problem.
But surely there is merit to death of the author, right? Well of course. If we were to account for the creator's intentions in every one of their creations then we'd never be able to enjoy anything. And like I said, even a terrible person is capable of making something good, and they're very good at concealing their true nature from the public eye. What matters then is how you act once their shamefulness is brought to light. Whilst the creator can inject their own politics into their creation as I've stated before, if they keep the two separate, then the onus shifts onto you if you wish to continue supporting them. And really whether or not it's worth it could depend on the level of the offence. For instance, if you're willing to consume the media of a known virulent anti-Semite whilst maintaining the idea that you don't agree with their views with full knowledge that they're still gonna profit from the consumption of their product, then you're still responsible for platforming them. And if they're still turning profits with their vile opinions out to the public, that tells them that they can say whatever bigoted bollocks they want and no one will care. With people like Ian Watkins and Gary Glitter, still listening to either of their music has a gray area to it; whilst both of them are detestable child predators, neither of them profit off of their music anymore, so you aren't platforming them. On the other hand, are you really still comfortable supporting the work of child molesters? Sure, their music might be good to you, but it's still a question worth thinking over.
At the end of the day, separating art from the artist is reliant on whether the art still platforms the artist or not. And let me be clear here; I in no way intend to cast a shadow of guilt over anyone who supports the art of otherwise problematic creators. I'm a massive Ozzy Osbourne fan, I know what it's like to support a controversial figure. Enjoy what you like, take your favourite elements out and enjoy them on their own if you have to. But please don't take the route of attempting to divorce the content from the creator through means of embarrassing mental gymnastics. It just makes you look more ridiculous than anything else. Now if you'll excuse me, I'm off to watch a James Bond flick. Ian Fleming all the way.