Hi, Cynthialee. I'm not sure, but I don't think UK newspapers use AP; I think they use BBC. Not that I know the BBC guidelines! But the last time I looked, the AP was asking writers to base pronouns on the subject's public persona. So when a person is presenting as female (before coming out, for example), then the birth pronoun is used.
There is one very clear mistake in which "she" is wearing a blue mortarboard; perhaps the copyeditor got confused. Other than that, I find it hard to tell whether the intermittent use of "she" is consistent with AP guidelines. I understand why, for PR and educational purposes, the article opens with "she" and then eases readers into "he" later. I understand why "she" is used to refer to Stephen when he was clearly living as a girl. I even forgive the reference to him as "she" in the last line because that sentence presents his father's perspective; the meaning would have been completely changed if the author had used the male pronoun.
Other uses of "she" are ambiguous because I wasn't always sure whether Stephen was presenting as female at the time in question. I presume that the reporter knew, but perhaps not. I don't know how much of a public presence Stephen had at that time or how he was presenting publicly.
I myself prefer male pronouns throughout the life chronology, but I can only claim that for myself. And I claim it because I was always male, no matter how other people saw me and no matter how hard I tried to fit in during certain phases of my life. AP guidelines don't recognize such positions, and a lot of individuals don't agree with them, either.
I concur that the article is a messy pronoun nightmare. But I'm not sure it could be improved all that much and still do the job within AP guidelines. I would be interesting in your input, though. It's a tough problem, I sure as heck don't have all the answers.