In Manhattan’s chi-chi Sant Ambroeus restaurant, the pair of smartly dressed women at the next table are making not-so-surreptitious “eek” faces at each other, having clocked that their neighbour for lunch is Taylor Swift. And that’s nothing compared to the commotion gathering outside: wherever Taylor Swift dines, a swarm of fans and paparazzi soon forms on the pavement.

This is normal life for the biggest force in pop right now, a global superstar whose songs soundtrack lives, whose tours sell out stadiums in seconds, and whose every facial expression generates a million tweets. Taylor Swift in 2014 is an extraordinary phenomenon. She began as a ringletted country singer, teenage sweetheart of the American heartland, but between 2006’s eponymous first album and now she’s become the kind of culturally titanic figure adored as much by gnarly rock critics as teenage girls, feminist intellectuals and, well, pretty much all of emotionally sentient humankind. Unlike Beyoncé with her indomitable run-the-world warrior-queen stylings, or Nicki Minaj, with her cartoonified, amplified self and pantheon of alter egos, there is very little image-making going on with Taylor Swift, pop star. Instead, it’s her “realness” that’s made her; as well as, of course, some clever choices and heavy doses of charisma and songwriting talent. She is, as her friend the teenage media magnate Tavi Gevinson put it, nothing less than “BFF to planet Earth”. Which, for one thing, entails talking to planet Earth at a moderate volume.

“When I’m doing a concert, it’s not like, ‘WHAT’S UP LONDONNNNN!’ I pretty much just speak at this level,” she says. As a result, her stadium shows have the confessional good feeling of mass sleepovers and she communicates with her vast audiences “as if I’m talking to them across the dinner table”.

Swift releases an album every two years without fail, which means it’s time for a follow-up to 2012’s Red. We meet in the week before she announces new album 1989 and its lead single, Shake It Off, a breezy, uptempo number about ignoring the haters. She explains: “In the last couple of years I’ve had to come to terms with the fact that anyone can say anything about me and call TMZ or Radar Online or something, and it will be an international headline. You can either go crazy and let it make you bitter and make you not trust people, and become really secluded or rebellious against the whole system. Or you can just shake it off and figure that as long as you’re having more fun than anyone else, what does it matter what anyone else thinks? Because I’ve wanted this life since I was a kid.”

Her cheery, stoical take on celebrity and tabloid intrusion has served her well. “I am not gonna let them make me miserable when I could be enjoying my life,” she says. “That’s why you see these artists become a tabloid regular and then become artistically and musically irrelevant, because they let [gossipy websites] stifle them. It’s not going to happen here.”

For the Shake It Off video, she enlisted 100 fans as well as a load of professional dancers: “Ballet dancers, breakdancers, modern dance, twerkers – and me, trying to keep up with them, sucking.” She adds: “I feel like dancing is sort of a metaphor for the way you live your life. You know how you’re at a house party and there’s a group of people over there just talking and rolling their eyes at everyone dancing? And you know which group is having more fun.”

Dancing enthusiastically amid hauteur has become a Swift trademark; specifically, letting loose at awards ceremonies while everyone else remains seated and stiff. She’s been attending these shows since she was a teenager and, after “eight years of these very stressful and competitive scenarios, sitting in the front row trying to figure out how you’re supposed to act”, she eventually realised that “I can process this as a huge pressure cooker or I can just look at it like I have a front-row seat to the coolest concert right now.” Dancing to Justin Timberlake with Selena Gomez at last year’s VMAs was a particularly fine example of the latter.

But her most famous awards-show moment remains Kanye West’s interruption at the 2009 MTV Awards. Such is Swift’s global standing that the President himself called West “a jackass” and, five years on, the moment still hasn’t quite died in the collective imagination. Or indeed, Swift’s own: Last year, she gave her friend Ed Sheeran a jar of homemade jam with a handwritten label that said: “Yo Ed Im really happy 4 u and I’m gonna let u finish but this is the best JAM OF ALL TIME - T.”

In short, the interruption only magnified good feeling towards her. Less fortunate was her Grammys appearance the following year in which she wobbled her way through a duet with Stevie Nicks and subsequently suffered an online shellacking. At this year’s ceremony, she seemed determined to eclipse that with a rendition of the bruised All Too Well, a song allegedly inspired by her relationship with Jake Gyllenhaal. Her performance was fierce and focused. When she finished, she turned from the piano and faced the audience with an intent gaze of defiance and held it for several seconds. The message was clear: no more the victim. It’s this song, incidentally, that contains one of the lyrics she’s most proud of: “‘You call me up again just to break me like a promise/ So casually cruel in the name of being honest’”. She pauses, pleased. “I was like, I’ll stand by that one.”

All Too Well was taken from 2012’s Red, an album defined by widescreen, wind-machined renderings of heartache, which confirmed that “country” could finally be dropped from her tag of “country-pop” singer. But 1989, as she explains, is shorter on the “jilted, sad, pining”. Instead, “it’s the phase after that, when you go out into the world and make changes in your life on your own terms, make friends on your own terms, without [literally] saying ‘C’mon girls, we can do it on our own!’”

Taylor Swift performs onstage during the 56th Grammys, January 2014. Photograph: Kevork Djansezian/Getty Images Photograph: Kevork Djansezian/Getty Images

Those words will kindle the hopes of those who’ve suspected Swift has experienced some sort of feminist awakening over the last few months. Recently, she was spotted browsing the feminist section of a Manhattan book shop. Even more heartening has been the array of BFFs filling her Instagram feed, Lorde and Lena Dunham among them. This seems to be one of the many fun things about being Taylor Swift: that pretty much any smart and interesting young woman in the public eye is yours for the friending. She loved Lorde’s debut album Pure Heroine, so sent flowers to congratulate her on its release. Lorde, in turn, got Swift’s number from Gevinson (whom Swift recently counselled through her first heartache) and sent her a long message apologising for once calling her “too flawless to be a role model”. Unsurprisingly, Swift forgave her. The first time they hung out, she says, “We took a walk and sat in the park and ate Shake Shack burgers.”

Her friendship with Dunham began even more simply. Swift had tweeted in praised of Girls, and the moment she followed Dunham on Twitter, Dunham responded with a direct message which said, “something like, ‘Can we be friends please?’ And then that was that.”

Has female friendship become more important to her than romance? “Without a doubt. Because the other alternative” – as in having a boyfriend – “isn’t really possible right now. It just doesn’t seem like a possibility in the near future. It doesn’t ever work. What works is having incredible girlfriends who I can trust and tell anything.”

As for the endless “is Taylor Swift a feminist?” pieces – well, they can die now. “As a teenager, I didn’t understand that saying you’re a feminist is just saying that you hope women and men will have equal rights and equal opportunities. What it seemed to me, the way it was phrased in culture, society, was that you hate men. And now, I think a lot of girls have had a feminist awakening because they understand what the word means. For so long it’s been made to seem like something where you’d picket against the opposite sex, whereas it’s not about that at all. Becoming friends with Lena – without her preaching to me, but just seeing why she believes what she believes, why she says what she says, why she stands for what she stands for – has made me realise that I’ve been taking a feminist stance without actually saying so.”

I ask if tabloid scrutiny over her lyrics (and the string of famous exes they allude to), has dissuaded her from pursuing what rock critic Robert Christgau calls her “diaristic realism”, or the clues she famously leaves in her liner notes. No, she says, because it’s that sense of reading a journal that “has always connected me to my fans in this very intense way”. Nonetheless, she concedes that “it’s an interesting tightrope walk to write autobiographical songs in an age where mystery is completely out the window”.

With Kanye West at the MTV Video Music Awards in 2009. Photograph: Jason DeCrow/AP Photograph: Jason DeCrow/AP

The way she sees it, there’s a gender element to such scrutiny. “I really resent the idea that if a woman writes about her feelings, she has too many feelings,” she says. “And I really resent the ‘Be careful, buddy, she’s going to write a song about you’ angle, because it trivialises what I do. It makes it seem like creating art is something you do as a cheap weapon rather than an artistic process. They can say whatever they want about my personal life because I know what my personal life is, and it involves a lot of TV and cats and girlfriends. But I don’t like it when they start to make cheap shots at my songwriting. Because there’s no joke to be made there.”

True: Swift has always been a deft lyricist. Our Song, for example – a perky early hit written when she was 16 – indicates her precocious skill when it reveals itself as the “our song” of the title: in the last verse she sings, “I grabbed a pen/ And an old napkin/ And I wrote down our song”.

The hysteria and scrutiny came later, with songs like 2010’s Better Than Revenge. Fired at the woman who took her man, rather than the man himself, it includes the snide, “no amount of vintage dresses gives you dignity” and a chorus that’s distinctly unsisterly: “She’s an actress, whoa/ But she’s better known for the things that she does/ On the mattress, whoa”.

For a moment, Swift seemed in danger of typecasting herself as a victimised prude. “I was 18 when I wrote that,” she reminds me. “That’s the age you are when you think someone can actually take your boyfriend. Then you grow up and realise no one take someone from you if they don’t want to leave.”

We’re meant to assume that anyone making this much money (at Forbes’s estimate, she’ll have raked in $64m this year) or anyone this astronomically successful (seven Grammys, a Country Music Association lifetime achievement award when she was 23, and so on) must be a cold-blooded and ruthless operator. But Swift’s reputation for niceness is unrivalled – and, as I discover a few minutes later, completely deserved.

“It’s always been important to me, that’s always been a priority,” she says. “Every artist has their set of priorities. Being looked at as sexy? Not really on my radar. But nice? I really hope that that is the impression.” She agrees that “nice” is often used pejoratively. “Totally! But I don’t care if that’s not cool, to seem nice or not. I’m not that focused on being cool and I never have been.”

Outside, a sea of big black cameras and upraised iPhones are aimed at the door that she’s about to walk through. After a glance through the windows she wraps her arms around me in a very deliberate hug goodbye. Then she looks me in the eye and says, in a low voice: “Are you ready for a photoshoot? Take my hand.”

Shake It Off is out now; 1989 is out in October

• This article was amended on 25 August 2014 to remove a tweet that was wrongly attributed to Taylor Swift and replace it with a message she wrote to Ed Sheeran.