I did a podcast with Fox where we looked at every Disney Animated Canon movie ( canonball.invincible.ink/ ) and got to consider what I, a millenial adult with a lifetime of brain worms from an oppressive cult thought of the Disney Animated movies that define Disney Adults and Disney Magic and the Cultural Zeitgeist and if you're not familiar with my opinion of these, almost all these movies are terrible. I dislike them often in terms of their ideologies, their moral and ethical positions - like, not just the invisible ink elements, but often, a lot of the things in them that they very clearly, explicitly want to be true.
The big one is The Lion King.
In the podcast, I describe that my hate of the Lion King is unique in that I think it's the first Disney movie I hate because of things it advocates for. Like it's one thing to hate how Cinderella thinks the most fantastic thing you can do with magic is have a single nice party night, and that's not a responsible use of power, but it's another thing to hate The Lion King because it's a movie that wants to talk about how some people are born to rule and everyone else exists to be eaten; you see, when we die, our bodies trickle down and become the grass, etcetera.
This is an instance of a rare time in the podcast where what I considered was intrinsic critique; within the context of the text, the text is presenting something that I think sucks and I don't like.
But then when talking about The Black Cauldron, a much less enjoyable movie with more stilted bits and worse songs and characters, I was a lot more fond of it, because to me, the things that stood out was stuff the movie tried to do, and failed at, and part of how it failed were things that Disney did to actually damage the movie, like, cutting chunks out of it. That's what I think of as extrinsic critique - not looking at the text but the circumstances of how it was made and the things that it might have been doing or trying to do before the final product existed.
My other normal examples of criticism is Avatar : The Last Airbender, where I have intrinsic critique (the story chooses to build to a point where it expresses that maiming and prison is better than killing fascists) versus The Legend of Korra, where I have extrinsic critique (thanks to the standards of the people allowing the series to exist, every series is rushed and also a queer story gets near-invisibled). These are two different ways to see problems in a story, and neither of them forgives the other. Korra is a rushed story with a recap episode that has to repeat a plot arc of Korra Learning Humility and not enough Korra Kicking Ass, and Aang's story doesn't culminate with him shooting fire hitler in the head because he's fucking twelve and the story is for little kids! Both of those things make complete sense.
In a lot of ways queer media gets crushed in between these things, too; there are extrinsic factors fighting for queer media's right to get to exist. The Owl House is a series I love and I feel at times very 'no notes' about, even though the final season and specials are absolutely rushed. But that extrinsic criticism (I wish there was more of it) isn't the same thing as intrinsic criticism, even if it informs it.