When it comes to "problematic things I enjoy anyway," my biggest guilty pleasure is East Asian dramas. Typically Japanese ones, as that's the language that I (sort of) speak, but now I've started to study Chinese, I've added those to my viewing line-up too.
Most recently, I've been watching a very silly Taiwanese drama called Miss In Kiss, which is a remake of a remake of a Japanese manga called Itazura na Kiss, or Mischievous Kiss. The show's tropey romcom set-up is pretty typical of these sorts of dramas -- the girl (Xiang Yue, in this version) is in love with the smartest and most popular boy in school, but he dismisses her as too stupid to pay attention to. When her house is destroyed in an accident, she and her dad move in with her dad's best friend and his family -- including her crush. Misadventures ensue.
It can be a fun show to watch. The bright colors and zany adventures are definitely refreshing compared to a lot of western dramas. But the supposed love interest is consistently a cruel jerk to the protagonist, and any vague sign of decency on his part is treated as a Hint of True Love. Meanwhile, another guy decides that he has ownership over the protagonist, because he loves her, and so he calls her father "dad," insists they're basically married, and plans his life around "protecting" her and building comic schemes to kickstart their love.
If you've never seen East Asian drama, this sort of set-up is pretty par for the course. I'd love to argue that there's some hidden feminism in watching these shows, but nope. Although not every drama is like this, many of them are, and whenever I watch them, it's with the knowledge that I'm enjoying the lighthearted drama and practicing my language skills at the price of attempting to ignore pretty consistent narrative misogyny.
I'm not sure if it's just because it's been a while since I watched one of these dramas, but Miss in Kiss seems particularly bad. We've got the "they MUST be together" trope, despite the guy's indifference and cruelty to her. We've got the forceful hand slamming into the wall beside her head (multiple times), the grabbing her by the wrist to pull her around (multiple times), the guy she's not even interested in getting violent to protect her honor from the guy she likes (multiple times) and basically acting as a stalker (almost every episode). It's a really messed up representation of romance. And sure, it's a silly show. But it's uncomfortable to dismiss those elements as "well, that's just the genre," even though, in many ways, that is the genre.
I hit my limit about 20 episodes in, when the "oh my god, are you kidding me??" elements overwhelmed any possible benefits, and I quit. I wouldn't have even lasted that long if I didn't desperately need the practice listening to fairly straightforward Chinese. But as I spent my days writing about feminism in media and spent my evenings watching this "lighthearted" but messed-up romance, it got me thinking, again, about what it means to watch something that you know is problematic. I don't just watch these series for language practice. I enjoy them. I like the music, the bright colors, the often farcical plotlines, especially the epic melodramatic romantic moments. My favorite in college was Hana Yori Dango, which has such gems as "guy and girl get trapped in broken elevator" and "guy gets amnesia," as well as the familiar arc of "guy is horrible to protagonist but actually they're in love." I watch for pure entertainment value, with bonus learning on the side. But I've watched many of them while studiously ignoring certain elements, and quit several when those elements got too much.
I think, for me, it depends how far the story takes these elements, and how integral they are to the plot. These dramas aren't doing anything particular new with their sexist plots, and they're not doing anything that feels like it was taken from the 19th century either. These are all very familiar tropes, in series full of familiar tropes. They fit comfortably in that context, so it's much easier to ignore them and accept them as just part of that sort of show. And we are all experts at ignoring run-of-the-mill sexism in entertainment. It's presented as normal, so we either take it as normal, or accept it as a price for watching whatever the most popular shows and movies of the day are.
And so, honestly, I've trained myself to accept a certain level of "weak girl, controlling guy" sexism in my East Asian dramas, just as I've trained myself to often watch American series with two brains -- the "I'm enjoying this" brain, and the "critical thinking" brain. And the same divide comes into play here. If the sexism is emphasized too much, or plays too big a role, I may quit, but a certain level of it... well, if I was writing about the show, I'd analyze it to death, but if I'm just watching for light entertainment, I often accept it as an unfortunate price of admission. I don't really think that's a good thing, but perhaps it is a necessary one.
But if anyone has any recommendations for any cute but non-sexist dramas in Japanese or Chinese, I'm eager to hear about them! Especially if they're on Netflix. :)