Antony and the Johnsons performing in Australia in 2012. On the 2005 breakthrough album, I Am A Bird Now, recorded under her group's name, Antony and the Johnsons, she sang about loneliness and domestic violence, guilt and shame, transformation and liberation. The lyrics laid her vulnerability and longing bare, but they were also a self-consciously political act. She brought transgender performers from New York with her on tour, to be admired as she sang, challenging the audience's notion of feminine beauty. You can't be an LGBT rights activist without being a feminist, she argues, and you can't be a feminist without trying to save the world. "I draw a line between the struggle of a gay child in Afghanistan and ecocide – it's all part of the same story … My goal, more than anything … is not to change people's minds, but to galvanise and encourage the people whose minds are already clear."

Anohni, formerly known as Antony Hergaty of Antony and the Johnsons, is coming to Sydney. Credit:Alice O'Malley As a journalist interviewing Anohni, the name she has used for just over a year, it is wise to be aware that she is not much interested in talking about herself, and that questions about her gender identity are off limits. She was born a boy and grew up to become a beautiful woman, as she sings on For Today I Am A Boy. Her transition, or lack of it, is none of your business. When I broach the subject of hormone therapy, after half an hour of amicable conversation, she politely shuts me down. The transgender equality movement has made significant advances in recent years, but visible progress obscures continued violence and prejudice. Former Olympian Caitlin Jenner is on the cover of Vanity Fair, Orange Is The New Black star Laverne Cox is on the cover of Time, but more trans women of colour were murdered last year in the United States than ever before.

Our brokenness as a species is beyond being an issue at the moment. Anohni "If you're 15 and you want to go online and see pictures of other trans kids, you can do that now, whereas 30 years ago, you'd be groping in the dark for anything, and it wouldn't necessarily mirror you or your story," Anohni says. "It was a lonelier experience. Not that it isn't a lonely experience now, but I do see a lot of young people that are empowered around the issues of gender identity." Growing up in the English town of Chichester, then as a teenager in California, she scrabbled for whatever information and encouragement she could get. In 1990, she moved to New York and found a community that accepted and understood her. An "obsessive historian", she learned about artistic forbears such as the Cockettes and the Hot Peaches, and sought out the drag queens she'd seen on Mondo New York, a documentary about the Alphabet City cabaret scene.

Together with Johanna Constantine, she founded Blacklips, a variety troupe with a bawdy, confrontational aesthetic fit for a transgender community reeling at the peak of the AIDS crisis. Late at night at the Pyramid Club, they sometimes threw offal at their audience. At school, she had developed her unique singing voice by copying artists she admired, including Boy George, Alison Moyet, and especially Nina Simone. The revelation that came to her over long days at the piano was that the more personal her songs were, the more people they touched. "I would literally be sitting there crying and singing all the time," she told Debbie Harry, in Interview magazine. "The goal for me at that age was just to be as close to crying as I could be while I was singing." Antony and the Johnsons, named for transgender activist Marsha P. Johnson, could easily have remained a underground legend, beloved by the cognoscenti and unknown outside downtown Manhattan. But then in 2003, a copy of their EP, Fell In Love With A Dead Boy, found its way to Lou Reed. Reed took Antony on tour, to sing backing vocals, and their duet on Candy Says, his song about transgender Warhol superstar Candy Darling, became a highlight of his gigs. He promoted his new friend tirelessly, telling reporters, "When I heard Antony, I knew that I was in the presence of an angel."

On Hopelessness, Anohni's voice is as beautiful and sad as ever, keening to the musical firmament created by producers Hudson Mohawke and Oneohtrix Point Never. "I wanted to do something that had a seductive sound, using contemporary pop language, and then embed within that this hardcore, very direct language," she says. "Not dressing anything up or hiding it. Just saying what I really feel." The lyrics veer from anger to despair. "Drone bomb me … blow my head off," pleads the opening number. One track has "Execution, it's an American dream," for a refrain. Another addresses the surveillance state: "I know you love me, because you're always watching me." The human race is presented as a virus attacking its host cell, the earth. In 2013, Anohni spent 10days living with the Martu of Parnngurr in the Western Australian Desert, and she has since campaigned against a proposed uranium mine on their ancestral land. "What's happening in Australia now is a free-for-all. It's a gold rush," she says. Despite her advocacy, including a high profile appearance on ABC's Q&A, the mine looks set to go ahead. The federal government has granted conditional approval to Cameco and Mitsubishi to dig at Kintyre, inside the Karlamilyi national park.

Four Degrees, a single released to coincide with the Paris climate conference, is a stunning meditation on our complicity in global warming. To a hammering synth track, Anohni fantasises about seeing dogs crying for water and lemurs burning in the trees. "It's only four degrees," she sings – a benign-sounding rise in average temperatures predicted by many climate scientists, that would have disastrous consequences for the planet. Ecological destruction has been the second great theme of her career. On Another World, from her third album, The Crying Light, she lamented that "this one's nearly gone". Manta Ray, a track she wrote with J. Ralph for the documentary Racing Extinction, was nominated for an Oscar this year. There were five nominees in the Best Original Song category, but only Sam Smith, Lady Gaga and The Weeknd were asked to perform. In an open letter published on line, Anohni declined her invitation to sit with the Hollywood aristocracy.

"I will not be lulled into submission with a few more well manufactured, feel-good ballads and a bit of good old-fashioned T. and A.," she wrote. "They have been paid to do a little tap dance to occupy you while Rome burns." It was quite an RSVP. This refusal to be co-opted is evident throughout Hopelessness, in particular on a track about Barack Obama, a president Anohni campaigned and cried for. Seven years into his administration, her sense of having been deceived is acute. The song is a dirge of his name and a list of his perceived crimes, from executions without trial to punishing whistle-blowers. "It's as much an indictment of my own naivety. 'Like children we believed'," she says. "Obama ran on a platform of transparency. The only person that's in prison for war crimes is Chelsea Manning – the one completely powerless American soldier that had the moral courage to call it out. "Would Obama have the moral courage to pardon her when he leaves office? Not if he wants Hillary to win."

What about you? I ask. Would you like Hillary Clinton to win? For years, as a co-founder of the Future Feminist Foundation, Anohni has campaigned for "a shift towards more feminine systems of governance", starting with more women in positions of authority. "It's the last time I'll get suckered into identity politics as a reason to vote for someone," Anohni answers. "If Hillary's the first woman president, well, in England we already know what a Margaret Thatcher is. It's not an end unto itself to be the first woman president." So what would it take to usher in real change? Is she talking about a revolution? As ever, she resists easy answers, preferring to respond with a question of her own. "Our brokenness as a species is beyond being an issue at the moment. We're totally out of control," she says. "The only question that remains is: 'Is it possible to change our trajectory?'."

Anohni plays the Sydney Opera House from May 27-31 as part of Vivid Live, as part of a bill that includes New Order, Bon Iver, Esperanza Spalding and Max Richter's Sleep.