I think GRRM does a nice job with this.If gender is an issue in your world, your character's gender will be a facet of who they are and how they relate to the world.
I don't know if he's a sexist, a feminist, or if he's as gray in this area as some of his characters are in the between-good-and-evil sense. But just on the merit of his writing...
His world (in ASoIaF) is a very sexist world, horrible for either gender, really, but women are definitely objectified there. The expectations are different for each gender, and even crime and punishment is different. ("Take the Black" vs. "Walk of Shame")
You see clear physical differences that are often as expected for each gender, but you have characters that beat those odds: Arya outperforms boys her age in skilled combat, and Brienne is stronger than most men and highly skilled. Her trainer taught her to use male pride (as in "I can't lose to HER!") to her advantage.
Tyrion is a strong character, but not physically strong. A non-dwarf/non-cripple who lacks "manly muscle" is Sam, who is not only out of shape but also has an internal battle with cowardice. The world expects Sam to be strong because he is male. Another expectation of a man is seen when a virgin prince wants to marry a widow. His bodyguard warns him that he'll look weak, since the widow is obviously experienced. So of course the prince finds a way to look "strong."
I don't know if GRRM is overrated or really just that good, but where his writing fits in with this conversation, I think he's a writer to emulate. He has a decent gender mix of strong, weak, good, evil and "gray" characters. Gender is an important part of the character, whether it's biological or societal, and those "explanations" do eventually show up (like Brienne recalling her trainer's advice on male pride), but it isn't really needed to sell the character...
What I read in his books aren't gender-bent characters successfully explained.
I read about interesting characters with interesting arcs.
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