I've heard that Fury Road is both extremely feminist and extremely anti-feminist at the same time. It stars a bunch of strong women fighting for their own destiny... but they're also half naked lingerie models.
I haven't heard the latter side argued, and I don't think it makes a lot of sense. The Brides were specifically selected by Immortan Joe for their beauty, and he didn't give them a lot to wear. But that wasn't gratuitous titillation, it was a reflection of the objectifying attitudes they were fleeing from. And they weren't glamorized and leered at by the camera, but were allowed to get dirty and scratched up, and they had individual personalities so they weren't just there to look good. And Max didn't try to hit on them or objectify them or ogle them, but just treated them first as obstacles and then as allies.
So what's a strong female portrayal? I always strive to have prominent positive female characters in my stories and I always wonder if I'm doing enough to that end.
As Gail Simone and others have said, "How do I write strong female characters?" is the wrong question. The question is, "How do I write strong characters?" Being male or female is just one facet of who they are. The rules for effective characterization are the same either way. Treat them as individuals rather than generic classes. Give them distinctive personality traits. Make them nuanced and flawed rather than idealized. Make them active rather than reactive. Give them an inner life rather than just looking at them from the outside. If you go in thinking that the way to write women is fundamentally any different than the way to write men, then you're already failing.
And it's not just about physical strength or being a fighter. It's about strength of character, or simply being interesting enough to leave a strong impression on the reader.
I often hear about a character "having agency", controlling his/her own life and not existing as a component of another stronger character. Someone who does what she wants to do, and not what a man in her life wants to do, etc, etc.
Basically, yes, but even people in nominally subordinate positions can have agency. Look at history -- beyond the traditional male-centric way of writing it -- and you find lots of ways in which women found agency within the context of male-dominated societies, e.g. controlling household finances or marriage decisions. Many oppressed groups -- women, racial and religious minorities, slaves -- have had agency in the subtle ways they resisted oppression and held on to their traditions and identity.
Agency is essentially about getting inside a character's head, seeing how they think about the situation they're in and what choices they make in reaction to it. No matter how powerful or powerless people's nominal position may be, they still have opinions and reactions and choices, and if you let your characters have those things, then they have agency. An agent is simply one who acts, rather than purely being acted upon.
https://en.wikipedia.org/wiki/Bechdel_test
And of course there's the Bechdel test. There must be at least two female characters and they must talk about something other than a man.
That's not a "must," per se. There are effective female characters in stories that don't have any other women, e.g. Sandra Bullock in
Gravity. The Bechdel Test is meant more as a commentary on gender representation in media in the aggregate. An individual story passing or failing the test doesn't necessarily mean it's feminist or sexist, respectively, but if the majority of stories fail the test, then there's a systemic problem that needs to be addressed. Bechdel isn't a strict litmus test, more a rhetorical device to get us thinking about inclusion and representation.
The point, really, is that most movies have more than two named male characters who talk about things other than the opposite sex, but a lot fewer have the same with female characters. And that's because too many movies treat men as the default and women as an afterthought. If you just write the sexes equally, then the Bechdel Test takes care of itself.
But what's the line between including M/F relationships and romance in a sensible way and going too far? What defines a positive feminist M/F relationship?
The same thing that defines a healthy relationship in real life -- equality and respect for both participants. Both points of view being paid attention to. Both parties being treated as individuals who have full lives of which the relationship is just one part.
And of course one wants to avoid stereotypical overly emotional portrayals of women. But what's the line there? Should we strive to be gender neutral, where the gender is utterly irrelevant to the personality? For example Starbuck in NuBSG.
I don't think there's anything wrong with emotionality in either sex. Characters can be passionate and vulnerable but still strong. Again, don't try to define this in terms of types or categories. Treat each character as an individual. Approach them from the inside, try to see the world as they would, like method acting. Give them personal, individual reasons for their emotions and reactions.
And if you have trouble imagining how women see the world, then for goodness' sake, make more female friends. Read more female authors. Just pay attention to what's already out there.
Should a "strong" female character mean aggressiveness and confidence? How much self doubt is allowed?
As I said, that's a common misreading. Personally, I think aggression and machismo show weakness rather than strength. And a lot of the time, strength in a character comes from overcoming vulnerability and doubt rather than simply lacking it. That's not about sex, that's just about characterization in general.
Female characters shouldn't be alike any more than male characters. Just write individuals -- that's what matters. Don't have a bunch of different male characters plus "The Girl." Have just as much variety of types in both sexes.