I think the action hero trope is less about sexism (i.e., having to recast a woman as competently aggressive) than simply that it's a particular genre of movie where story is told and conflict revealed and resolved through physical action. It attracts a particular kind of audience/mindset, and expanding it to include women was not necessarily trying to directly masculinize them (although it definitely can function that way), it was at least in part trying to expand the boundaries of who could be effective in that role regardless of gender.
I personally like to have drama mixed with my action -- some form of character depth and understandable even in a streamlined movie -- so when you look at a movie like Salt, for example, although Jolie is quite competent in the action sequences, I find the movie more compelling when it is exploring her relationship with her husband and how finding him is one of her primary motivations for much of the movie. In the scenes with just them, you acquire an understanding of her not just as a cold effective professional but her actual vulnerability and how much she had bonded with him after trying to shut herself away from emotional interactions for so long.
I can't believe no one has mentioned Marge Gunderson from Fargo. In a movie full of incompetent men, she's the one person who calmly takes charge and gets things done. All while being hugely pregnant.
I liked how "normal" she was -- just a woman doing her job, steady and consistent, while others floundered or got distracted. Totally unflappable.
A lot of female heroism seems subtle like that.
Still running through movies in my head, so maybe I will come up with better examples later. But sometimes female heroism is bearing up under a disadvantaging system. For example, in The Hours, one of the more compelling plotlines involves the '50's mother (Laura?) who -- crushed by the system around here -- does the unthinkable and walks out on her family, which includes her young son. This results in a lot of hate being directed her way decades later, and it sounds terrible, but once you see the scenario she lived in and how it was crushing the life from her, and how lesser means of escape failed, then you're left with just silent contemplation over an act that was severe and damaging and yet possibly the least destructive out she had at the time. In that case, it was her resisting the establishment that had been crushing the life from her rather than succumbing, despite the fallout from that. Meanwhile those in the establishment didn't change or grow; who the establishment could not control, it instead judged and condemned.
Or in Moulin Rouge, where you see Satine trying to balance everything -- building a life for herself professionally, having to play the "game" as a courtesan in order to get ahead, until she finds herself attracted to a young man who falls madly in love with her, threatening to upend the careful balance of her life. She wants him but will likely lose her career if she accepts him, and meanwhile the fate of the Moulin rouge and all her friends rest on her selling her life to a man who just views her as an object. And, yes, she's also dying but doesn't want to tell anyone and pretends she's fine, all as part of keeping the plates spinning. It's the typical battle of one's desires balanced against the needs of the community/family all over again, and trying to honor everything you can to the best of your ability, rather than just demanding straight self-interest. The system is stacked against you, and somehow you stay afloat while trying to honor the things you care about.
Again, there are better examples out there I am sure (which I'll recall when I go through my movie shelf), but Marge is such a great one. She's completely normal and rather heroic in her normalcy.
EDIT: Oh here's some more:
- Ree Dolly in "Winter's Bone"
- Mary MacGregor in "Rob Roy"
- Elle Arroway in "Contact"
