I don’t think it’s unreasonable to say that this kinda media really gets under your skin and ask if she’d be okay wearing headphones while watching it.
I have a similar relationship with romance reality and I’ve made it clear that I won’t hang out on the couch if that’s what’s gonna be on TV. I tell my partner he’s welcome to watch it all he likes, I’ll just do something else and that’s okay. He doesn’t like the Gundam or mecha shows I watch, so I can just say “hey man, enjoy your show, but this is ‘Gundam’ to me.” And that works as great shorthand. Sometimes he’ll say “oh I was more interested in cuddling with you on the couch than really watching something, I’ll change it” or “oh okay, I really wanted to catch up on this so you go have fun” and I’ll go cook or play a game or workout.
Maybe there’s a similar type of media preference you can reference to help your wife understand your actions.
Though while, ultimately, I think the onus lies on you to remove yourself from the situation rather than encourage your wife to change her behavior, it does sound like you’re trying to do that with your own headphones. At some point, it might be on you to get better at filtering the noise, but your wife might be willing to help you by wearing headphones. That doesn’t seem like a huge imposition to me, especially if it’s for something I’m listening to while doing chores or something. For her listening to clips of shows in between activities? Eh, I think your part of the headphone compromise would be grinning and bearing those brief moments.
Lastly, while I don’t think it’ll directly address this issue, it’s probably not a bad idea to do some introspection as to why this kind of media affects you so strongly. You clearly know what about it bothers you, but I’m sure you can think of other media types you dislike for a similar “moral disagreement” (for lack of a better phrase) that don’t elicit such a reaction. It’s nice to understand the things that trigger us in this way and why. Sometimes unpacking that makes them easier to bear and filter out, too.