A few points.
For those who see hormones and transgender surgery as essentially meaningless, I think you first need to take into account the biological reality that having an XX or XY chromosome set is not sufficient to determine maleness nor femaleness. Parts of the body can respond in atypical ways to hormonal cues set off by that chromosomal configuration. People need not even have XX or XY chromosomes. Rarely, people can even have both as a chymera fused twin. So their uterus, elbow and spleen might be XX, while the irises, nose, and testicles are XY.
The fact is that people can have intersexual bodies at the chromosomal level, the structural level, or as a result of various atyipcal development sequences or hormonal responses. Indeed some people argue that homosexuality is itself a form of this.
And the other fact is, our understanding is still incredibly primitive. Every year or two it seems a new research study comes out that shows some new observable aspect in our anatomy of the way in which our maleness or femaleness develops. For many people that development just isn't uniform and consistent at all. And for many people who exhibit uniformity or consistency, it may well be that is illusory, just because we haven't recognized enough of the nuances yet that would allow us to point out their uniqueness in a lab report.
Thus I certainly accept, and so should everyone else if they've followed even half the evidence, that intersexuality exists. It is not correct to say that all people are either male or female. It is not correct to say there is an easy and 100% reliable way to tell the difference. It is not correct to imagine that transsexual people are simply misinformed in their opinion about their own gender.
That being said, I am deeply sceptical of "Transitioning." Primarily because in accepting that everyone can have their own particular gender configuration, I don't think a person should then need surgery or hormones to "become who they really are." They already are exactly who they really are. And because it seems to feed into the idea that all people should be either male or female, as long as they are allowed to switch. Bullshit. I can't even stand people referring to the "opposite" gender. Nothing about gender is binary or opposite. It is all a great mish-mash of lovely unique humanity.
The reasons for surgery therefore become
a) to reduce the social burden of deviating from stupid outdated gender binary stereotypes that have been undermined in scientific minds by the kinds of reasons I already described
b) to indulge a certain appetite for cosmetic perfection by abandoning one's own perfectly reasonable body through invasive surgery.
My view of gender is that Bradley Manning already is who he is, and if she is a woman she already is. And if she is something much more interesting, which is an individual who need not be tempted into a boring gender binary, then "transitioning" should be discarded as unnecessary and limiting. Because of that, it should be really of no more significance that he wants to be called Chelsea than if he announced he wanted to change his name to Douglas.
As far as pronouns, in any conventional social situation, if I mistook a lifelong male's gender, or a lifelong female's gender based on some aspects of his or her appearance, it might create an awkward moment if I used the wrong pronoun. I do not imagine I would stand my ground and say "Oh yeah? PROVE IT." I'd just adapt to their correction and carry on. I'm sure I would extend the same normal social courtesy to Manning.
However there too I reject this "self determination" thing in principle. Just as I would not honour a gay or bisexual man's self-identification of "straight" when he gleefully and repeatedly sleeps with other guys, I reserve the same right to form my own opinion of anyone else's identity. This idea of honouring how people "self-identify" is frankly overblown.
So if we must have pronouns that are either male or female, I think what would be most comfortable and authentic for both myself and an intersexual person, would be to agree on which pronoun applies, coming to the same conclusion independently.
