Cigars I know I can't speak for anyone else, but it seems to be that most people are not saying gender is binary, but that sex is (albeit intersex also exists so perhaps not a binary exactly).
Sex is a neutral, no judgement-laden fact - it is what it is. Gender is thrust upon most people at birth and is assosicated with certain behaviours, characteristics, and restrictions. A lot of feminists believe that gender is purely a social construct.
(apologies if this feels like I'm explaining it to a 5 year old - I'm trying to get it straight in my head).
With regards to trans* issues and feminism, what I've got my head around is:
- all people are equal and are afforded human rights (because, obviously)
- some trans* people feel physical revulsion at their physical sexual characteristics and so change that medically. I can see the logic in this, in that if a major part of what you are identifying with is the physical characteristics, then changing those would alleviate some of the mismatch (sorry if that's not sensitively phrased, I can't think how else to put it).
Where it doesn't fit together for me is that a large proportion of the trans* community doesn't undertake to physically match their self-identified gender. What I am confused about is that if they are fine with their physicality, why they identiy as a woman. As I feminist, I think that gender is a social construct so there are no inherent attributes, qualities, interests, dispositions etc for either men or women, apart from 2 things: their physical sex, and the fact that their physical sex would have influenced most of the behaviour and expectations from the people around them, meaning that both boys and girls, men and women were constrained, restricted and policed, although women experience this hugely disportionately more given that they make up the majority of the population.
So I can't fit my ideas that gender is forced upon us rather than innate with the idea that we have "male or female brains" or that we have an inner "essential gender". If we're all just people who come in an infinite kaleidoscope of patterns and constellations then how can someone feel "like a man" or "like a woman"? Surely you can only feel what you are feeling, and not know how anyone else would feel? I'm really uncomfortable with this as I don't want to erase anyone's experience - I would genuinely love to know as something I just don't know.