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Promoting an artist's work is promoting the artist and their views.
The Harry Potter IP, for instance, is now the official flag of shitty transphobia, and hell will freeze over before I go waving it around or even stand under it.
It's not just a question of financial gain, it's a question of social impact and what we tacitly agree to tolerate.
Imagine, if you will, telling a rape survivor to just lie back and enjoy the masterful comic stylings of Bill Cosby, or at least to shut up while you watch it because they're ruining the funny, and YoU hAvE tO sEpArAtE tHe ArT fRoM tHe ArTisT.
What kind of message would that send? It would be telling them who you side with, it would be telling them that a rapist can purchase your undying loyalty and support just by being entertaining, and that as far as you're concerned, rape victims can just suck it.
It's not a good look.
Obviously, the worse and more immediately problematic the artist, the more pressing an issue this is.
The further back you go, the more unpleasantness you're likely to find, simply because social progress is a thing. But again in the case of JK Rowling, she's riding her popularity and influence in an attempt to drive trans kids to suicide right here, right now, which is just a leetle bit more pressing than the fact that some Victorian author was caught up in the casual racism of their day. Which is also not good, granted - but you triage these things.
Since you mentioned HP: seeing all the shitty views of Rowling coming to light also just destroyed my enjoyment of these stories. As a kid I used to love HP but now it just leaves a bitter taste in my mouth
I feel bad for my sibling personally. I at best thought the series was kind of fun but they were a massive Potterhead. We are however both different flavors of non-binary trans. My sibling is the kindest and most principled soul and seeing them go through essentially a grieving process made me fairly furious at the author not just for the shit she was spewing but the pain she was causing my younger sibling.