There are actors who leave you transfixed because of the sheer wattage of their star power, and actors who can suck you in so completely that you forget the person behind the part.

Cate Blanchett is that rare thing: an actor who does both. Whether freezing courtiers with a single glare in Elizabeth, the 1998 film that made her name, or hinting at a burning passion waiting to be released by the right touch from the right person in 2015’s Carol, Blanchett has a talent – and a presence – that is impossible to ignore.

This week, that range is on show in two very different television roles. On BBC Two on Wednesday she demonstrates charisma to burn as the conservative icon Phyllis Schlafly in the 1970s-set period drama Mrs America. Then, on Friday, she appears in an eye-catching supporting role in Netflix’s Stateless, playing the frumpy co-leader of an Australian cult, who claims to be able to transform lives through the power of song.

Put like that, it sounds almost humorous, an Australian version of Unbreakable Kimmy Schmidt, but Stateless, which was co-created by Blanchett alongside Tony Ayres and Elise McCredie, is far from a comedy. The six-part series is a complex tale of immigration, mental illness and detention, and Blanchett is a menacing presence in the life of protagonist Sophie (Yvonne Strahovski).

Stateless, with its dark, intertwining stories and refusal to offer up easy answers, showcases Blanchett’s willingness to immerse herself so fully in a role as to become almost unrecognisable. And Mrs America – in which she steals the show from such formidable actors as Rose Byrne, Uzo Aduba and Tracey Ullman (playing second-wave feminists Gloria Steinem, Shirley Chisholm and Betty Friedan, respectively) – highlights why, despite a refusal to court the system or spend much time in Los Angeles, Blanchett remains one of Hollywood’s biggest stars.

Schlafly, a self-described housewife and mother of six from Missouri, was in reality a highly educated activist who had already made waves in Republican circles thanks to A Choice Not an Echo, her 1964 polemic about the then Republican leader, Nelson Rockefeller. Determinedly anti-feminist, she rose to further fame in the 1970s thanks to a cleverly orchestrated campaign against the Equal Rights Act, which saw her convince American housewives that second-wave feminists were intent on denigrating their values and destroying their lives.

Blanchett first became aware of Schlafly, she told the Radio Times last week, after seeing her receive a standing ovation at a presidential rally for Donald Trump. “Then when she died [in 2016], Trump was at her funeral. And I was thinking, why? Then this project came along, so it’s been an absolutely fascinating journey for me.”

She was particularly intrigued by the way Schlafly manoeuvred her way through Capitol Hill’s male-dominated world. “I was gobsmacked by her ability to inspire, galvanise and mobilise people through various different tactics; she was an absolute force of nature.”

Where a lesser actor might be tempted to turn Schlafly, with her pastel twinsets and immaculate coiffeur, into a parody of conservative womanhood, Blanchett chooses instead to subtly hint at the ways in which the activist’s tough outer skin was formed by the slights she encountered as a woman operating in a masculine world.

Her Schlafly is the steeliest of magnolias, creamy smile permanently in place, even as she plots exactly where to slide the knife in, but she is also visibly hurt when asked to take notes at a meeting on a topic she knows more about than the men sitting beside her. It’s a beautifully calibrated performance, equal parts syrupy charm and fierce ambition, which never lets its subject off the hook, yet which is also rooted in compassion and understanding.

“I’m always interested in drama that explores the grey areas of life,” she told the Radio Times. “This is a non-judgmental series that asks myriad generations, ‘What do you think about this? How do you feel about that figure or that policy or that movement?’ It’s all about the conversation, and it’s so relevant. This show is like Groundhog Day – the discussions we were having back in 1971 and 1972 are constantly popping up in the media today.”

That she should be drawn to a character as complex, and as contradictory, as Schlafly is unsurprising. Speaking to the New Yorker in 2007, Shekhar Kapur, who directed Blanchett in Elizabeth and sequel The Golden Age, said: “The fluidity you get in Cate is also because of the contradictions inside her … [she has] the ability to be both vulnerable and totally ruthless.”

The writer of that piece, John Lahr, went on to note that Blanchett was “both candid and private, gregarious and solitary, self-doubting and daring, witty and melancholy”.

It is a theme that has been repeated throughout Blanchett’s career. In interviews, she appears warm and welcoming – happy to open her home to journalists and to talk engagingly about family life, from lockdown schooling to unexpected chainsaw accidents – yet also reserved.

Her reticence was formed in part during her childhood. The middle of three children raised in a close-knit family in Melbourne, Australia, Blanchett’s life was transformed following the death of her father, Robert, when she was 10. It was a tragedy that would reshape the family dynamic – her grandmother moved in to help her mother, Jane, a teacher, with childcare – and have a lasting effect on Blanchett. She has talked movingly about how she waved goodbye to her father, an advertising executive, on the day he died. In 2015, she told the Guardian that while she was loathe to make too much of his premature death, it had been a “very dark” time.

Her interest in acting was formed early, although she initially planned to become a museum curator, deciding to study drama while on a gap year in Egypt. “Acting had become like this terrible addiction. I felt I needed to give it five years and see where it took me.”

It took her to the very top as a successful stage career turned into eye-catching roles on Australian TV, and eventually film. She has won two Oscars, one for her pitch-perfect turn as Katharine Hepburn in The Aviator, the other for her portrayal of an unstable socialite in Woody Allen’s Blue Jasmine, and been nominated for several more.

Happily married since her mid-20s to playwright Andrew Upton, with whom she has four children, she appears to have struck the perfect balance between work and rest, regularly switching between film and stage and taking extended sabbaticals when needed.

Her film CV reads like a blueprint for how to have it all: a mixture of classy awards-bait, such as Notes on a Scandal, Veronica Guerin and Carol, and big-budget blockbusters such as The Lord of the Rings trilogy. For all her seriousness about the “craft”, she also has the ability to embrace the unexpected, stealing scenes as the evil stepmother in Cinderella, and making for a gloriously camp Hela in Thor: Ragnarok.

In part, that willingness to go over the top comes from the fact that she is a naturally generous actor, as attuned to the performances of those around her as to her own. Over time, and thanks in part to that role in Carol and her own fashion sense, she has gone from regal ice queen to Cate the great. The sense that she remains unknowable at heart only fuels the appeal. Perhaps that is why she is able to be both star and ensemble player. She has always performed on her own terms and for her own needs. As Kapur told the New Yorker over a decade ago: “Cate’s ruthlessness is with herself.” It is why she stands apart.