I mostly watch anime, but Madoka Magica does it. The nornal “Saturday Morning Cartoon” trope has some foreign being asking a child for help. One of the things this show does it acknowledge that maybe kids shouldn’t trust the first person asking for help. Towards pretty quickly, you figure out the character who’s asking for help doesn’t have the girls best interest in mind.

The MC of Cross Ange has several transformations through the show. First refusing “the call” from her commanding officer, then answering it, then realizing their CO is more interested in revenge then justice. It’s a pretty graphic show.

Goblin Slayer is framed as a standard JRPG/Table Top session, but the MC knows that if he leaves his “starter town” home, it will be over run by goblins. Also pretty graphic, but like Cross Ange, the first episode is the worse. BTW, despite being modeled on rpg tropes, there’s no rpg mechanics and the MC tends to do things not by what his class would dictate that would make a GM grown.

Not quite “Refusing the Call”, but in Reign of the Seven Spellblades, you realize that the MC came into the story with their own agenda. It’s an average anime, but if you find J. K. Rowling’s story telling annoying, you may like it.

I forget which season, but one of the Red vs Blue seasons starts with one of the characters becoming genre savvy and literally refusing any phone call coming in because they’re lazy.