Kate Bornstein has crammed a lot of lives into her 67 years. In no particular order, she has been: a man, a woman, a father, a husband, a performance artist, a novelist, a playwright, a gender theorist, a ship’s first mate, a sex worker, and a recovering Scientologist. She may be the closest person real life has to Virginia Woolf’s gender-shifting, multiple-existence character Orlando, only with cute round glasses and a Tardis necklace.

Bornstein’s next incarnation will be as a reality TV star, when the second series of Caitlyn Jenner’s show I Am Cait arrives next month. She has already been the subject of a 2014 documentary, Kate Bornstein is a Queer and Pleasant Danger, which did well at festivals, but entering the Kardashian world will be something else entirely. Although Bornstein did appear in the first series, which documented Jenner’s transition, she will now feature much more prominently.

Until very recently, transgender people were very much on the margins, invisible at best, mocked or attacked at worst. But transgender lives have suddenly become visible and celebrated – from Orange is the New Black’s Laverne Cox to Eddie Redmayne in The Danish Girl. It is wonderful, says Bornstein, over tea and biscuits in a London hotel, but it is still early days. “It is an amazing media moment for transgender people,” she says. “But that’s only one way of messing with gender. There’s non-binary, gender queer, agender, gender non-conforming. And no, that hasn’t reached mainstream.” It could take another 20 years before the rest of the trans community is recognised, she thinks.

Watch the trailer for Kate Bornstein is a Queer and Pleasant Danger.

Bornstein is currently in the UK touring her show, On Men, Women and the Rest of Us, which starts with her attending the funeral of her mother, and having to introduce herself to her mother’s friends, who hadn’t been told about her transition. It covers Bornstein getting to grips with existing somewhere between two genders: only someone as funny and charismatic as Bornstein could make a grammar lesson about pronouns so hilariously joyful (despite identifying as non-binary, she favours she, her, they and their).

The younger of two sons, Bornstein grew up in New Jersey. Her father was a doctor and the only thing that stopped theirs being a perfect 1950s nuclear family was the fact her mother wanted to have a job and trained as a teacher. Bornstein went to an all-boys school where, plump and Jewish, she had to deal with anti-Semitism and comments about her size.

Later, at Brown University, she discovered a love of the performing arts and became an actor. A good one, she says, and although she revelled in her ability to make people cry or laugh, she wondered what the point of it was. “I was looking for spiritual answers. It was the summer of 1969 and I was driving across the US, stopping at different religious communities.” She visited Amish, Baha’i and Kabbalah groups, then finally found the Scientologists.

All her life she had been puzzled about her gender – she knew she wasn’t a man, which meant, she thought, that she must be a woman. But she didn’t feel like a woman either and Scientology offered an explanation. “They said you’re not your body, not your brain, you don’t have a soul. You are your own immortal soul. And as an immortal soul, you have no mass, no energy, you don’t exist in time or space. Because of all of that, I thought, ‘Oh, then I wouldn’t have a gender.’” Scientology made sense to her. Unfortunately, she says, with a raised eyebrow and a sideways smile, “it’s a totalitarian cult.”

L Ron Hubbard had a fear of dentists, so his teeth were a mess and so was his breath

She was a Scientologist for 12 years. Three of them were spent as a lieutenant on founder L Ron Hubbard’s ship in his Sea Org fleet. “He was a physically unattractive man,” she says. “He had a deathly fear of dentists, so his teeth were a mess and so was his breath. Despite all of that, he made you feel like he was your daddy and you just wanted to please him. He would come out on deck at night, under the stars, and spin wonderful stories. He would tell us about who we were millions of years ago, the battles we fought back then, saying that now is our chance to move back in and free Earth from the slavery of the psychiatrists.”

She left after they subjected her to six hours on a lie detector machine, refusing a place on its punishing Rehabilitation Project Force. Instead, she chose excommunication, which meant leaving behind her then nine-year-old daughter, who is still a member of the Church of Scientology along with her mother, who hasn’t spoken to Bornstein since.

Following her exit, Bornstein suffered post-traumatic stress disorder. She was also coming to terms with transitioning, and finding that – after surgery – she wasn’t comfortable as a woman either. It wasn’t until she moved to San Francisco and found a transgender community that she became happier with who she was.

“I realised, ‘Wow, I have family.’ That made a big difference. Back in those days, anybody who was messing with gender was family with everyone else. We all hung out. Given a family, I felt strong enough to enjoy who I was. I think that’s still true to this day: I’d be a lot less sure of myself, a lot less active, if I didn’t have the extended family.”

Bornstein is writing her sixth book, this one about the infighting in the LGBT community – “and how to bring about some peace, as an elder”. But she is not universally loved within such groups: she has been criticised for referring to transgender people as “trannies” (affectionately, she says); and she has said sex work is “far from a bad thing”. Does she think the often vitriolic gulf between the group known as trans exclusionary radical feminists and transgender people will ever be fixed?

She is quiet for a while. “I think the only people who listen to trans exclusive radical feminists are transgender women. They call themselves feminists but it’s not the kind of feminist I ever knew. Who is paying attention to them? Seriously. So some people don’t think you’re a woman. So? It’s much more important to know you’re a woman than to depend on someone’s approval.” You only care, she adds, “if they are in positions of power”.

The last few years have been tough for Bornstein – she has undergone treatment for lung cancer – but her passion remains undimmed. A self-described “leftwing wing-nut and anarchist”, she is excited about the tantalising prospect of a Bernie Sanders presidency and, just before we leave, jokes about a no less tantalising prospect: how being a Kardashian cast member could lead to her own TV show. Please – someone commission this.

• Kate Bornstein is at Soho Theatre, London, 23-24 February.