If you have never been to Glastonbury, you will always get people telling you that “it’s just got a different vibe to other festivals, man”. Even platinum-selling musicians. “It’s like being in some weird medieval village,” says Ezra Koenig, frontman of Vampire Weekend, who had played Glastonbury three times with the band before going as a punter in 2014, when it finally clicked. “I stayed up all night and understood: this is very special. I can’t think of many festivals where there are old hippies who do their thing and keep to themselves, and keep that spirit of the 60s alive with arts and crafts. And there’s all the secret stuff you find in the woods, the various raves, little mini pubs everywhere ... Everybody’s walking through the mud and there’s a real communal energy to it. Probably a lot of them are on drugs, too.”

His band are playing their biggest-ever slot at this year’s festival, Sunday night on the Pyramid stage just before the Cure’s headline performance. They released their fourth – and best – album Father of the Bride in May, and like the previous two, it went to No 1 in the US and Top 3 in the UK. It came six years after the last one, Modern Vampires of the City, with Koenig having taken creative control after fellow songwriter Rostam Batmanglij left the band.

Vampire Weekend: Father of the Bride review – a scrapbook of brilliant ideas | Alexis Petridis's album of the week Read more

What has he been doing in the interim, apart from presumably contemplating how massive the universe is from a field in Somerset? “After three albums, things were threatening to become a little bit too professional for my taste,” he says. “When things get up and running, you are quite literally a company. You can reach this place where the marketing outpaces the creativity – it kind of feels like rolling the new car off the assembly line. I needed a few years to go back to feeling and acting like an amateur.” He wrote an anime series, Neo Yokio, which starred Jaden Smith and Jude Law; he also fell in love with the actor and director Rashida Jones, and they had a child. Koenig is at pains to point out the album was written before the kid came along. “Almost everything that’s been written about the album references my girlfriend and our baby, and I’m, like, I understand why, but …” He makes a frustrated “gnnnn” sound. “The timeline! Come on!” It’s the response of a man who, schooled in English and creative writing at New York’s prestigious Columbia University, has always been hyper-aware of how his band are portrayed.

We’re in a hotel bedroom that, being in London, is not big enough even for two chairs. Koenig, chic and handsome, sits cross-legged in the middle of a bed like the founder of a mindfulness app. The 35-year-old’s self-awareness stretches back to the band’s breakout in 2007, playing peppy guitar-pop influenced by west African highlife in preppy polo shirts and shorts. They were provocative in the slightly priggish manner of the well-educated, cocking a snook at the denim and leathers of the New York guitar bands that had come before them and flaunting their upper middle-class status. Blogs bristled.

“The conflict we engendered was performative class conflict,” Koenig says in perfect academese. “Deep down these people” – their then critics – “don’t care. Because real class conflict would be somebody saying: let’s really talk about this, about what percentage of critically acclaimed buzz bands come from privileged backgrounds. I promise you I wouldn’t place in the Top 30 in terms of intergenerational wealth. Maybe Top 50, but not Top 30.”

What about calling a song Cape Cod Kwassa Kwassa – in a world that’s more aware of cultural appropriation, doesn’t that now seem gauche? “If that song came out today we’d have just called it Cape Cod and slightly changed the arrangement, and nobody would have said anything,” he says. “There’s no easy answers, but you have to be thoughtful about it. There’s times when criticism helps you to be more thoughtful, and there’s times when it’s bad-faith clickbait. There are horror stories in terms of the way black musicians were treated and ripped off, and there are stories of black and white musicians creating music together that was part of a greater dialogue.” It would be in pretty bad faith to say Koenig isn’t in the latter category – he tracked down the son of Sierra Leonean “palm wine” musician SE Rogie to clear a sample on Father of the Bride, featured funk prodigy Steve Lacy on two tracks, and co-wrote Beyoncé’s Hold Up, a typically pop-culturally aware contribution that reworked a Yeah Yeah Yeahs lyric.

Facebook Twitter Pinterest Koenig, right, and Chris Baio at Coachella in 2008. Photograph: Chris Pizzello/AP

Those Ralph Lauren polos, so irritating to some indie rockers, were another bit of cultural commentary, this time on Koenig’s Jewish heritage. “I was like: don’t they understand that, for east coast Jews, Ralph Lauren is a really funny figure? He’s this guy from the Bronx who changed his last name. I tried to explain that, and for some people it went in one ear and out the other. Maybe it is asking too much of people to get into the hyper-specific identity politics of Jewish people.” Well, maybe, especially on your fifth afternoon cider. “I wish people would look at it through the lens I look at it through, but maybe no artist can really expect that.”

Father of the Bride closes with the elegant ballad Jerusalem, New York, Berlin. It references the Balfour declaration of 1917, which saw Britain set out Palestine as a home for the Jewish people. “I know I loved you then, I think I love you still / But this prophecy of ours has come back dressed to kill,” Koenig sings, setting his Jewish cultural pride against the infernal perpetual motion of the Israel-Palestine conflict.

I ask him to explain, and he is initially a little evasive. “Every identity has some degree of tension between victimhood and supremacy, nationalism and ... whatever the opposite of nationalism is.” He remembers a campaign at Columbia that accused Arab professors of antisemitism. “Having had personal experience [of antisemitism], I had an emotional attachment. But I was looking at the whole thing, and I could also relate to professors speaking their mind.” Perhaps there aren’t enough people who are so equitable. “Clearly not. But I don’t know if I was a politician I would be able to do that – it’s easy enough being a musician and just getting to think about things. You don’t have to answer any questions, all you do is pose them.

“I like to take the broad view – that all of these identities we hold so dear are blips on the radar of human history, and whatever ethnicity or religion we call ourselves, at some point an ancestor was probably forcibly converted, or would have had their family murdered. And now we call ourselves a proud member of the group. It’s funny.” He checks himself. “It’s not funny, it’s complex.”

The broad view narrows, though, when he talks himself around to the topic of the American Jewish community. “America has a duty to be an honest broker,” he says. “So if the whole Judaeo-Christian community is building some sick alliance out of Islamophobia, then I can’t stomach that.

“I don’t know what it’s like to go serve in the military when I’m 18, or to have had family members who were murdered when a bus blew up in Tel Aviv. But I do know what it’s like to be a Jewish person who grows up in New Jersey. So when I see a Jewish person who grew up in New Jersey talking about what the military needs to do and how evil the Palestinians are, I can easily put myself in their shoes and say: shut up. That is where the vast majority of my ire comes from. I can conclusively say: I don’t agree with you, I think you’re saying horrible things, I think your lack of empathy for the Palestinians is disgusting.”

Facebook Twitter Pinterest With Rashida Jones. Photograph: Todd Williamson/Getty Images

It’s not just politics that gets studied in Father of the Bride, but pop itself. It knowingly collides different tropes from across history: country music duets, jam bands, Laurel Canyon hippy folk, metropolitan guitar pop à la Paul Simon. “I write about romantic relationships, but that’s partially just because it’s a songwriting convention,” he says. You can imagine him sending Rashida a Valentine’s card, but only to poke fun at the heteronormative rituals of love.

Any postmodern cleverness is, however, made tuneful enough to wave a flag to at the Pyramid stage, and Koenig has learned to embrace the simplicity of the best pop. “A good Dolly Parton song gets at the ambiguity of the world way better than a song filled with strange images and expensive words does.” He compares the man who wrote Father of the Bride’s downbeat My Mistake with his younger “accusatory” self, “this person navigating this world: people who are more pretentious than me, assholes who want to take me down, idiots who try to tell me what to do, and people who treat me badly in relationships. Now that I’m older, a song like My Mistake seems more emotionally interesting to me: maybe it’s my own expectations that are what are bringing me misery, rather than you.”

For a band so associated with sun and shorts, there’s as much melancholy in Koenig’s songwriting, triggered by “relationship breakdowns, and then sometimes just depression and anxiety creeping up. That feeling of: did I do or say something that I can never fix, that’s going to haunt me for the rest of my life? Anybody who has dealt with depression and anxiety, which I think is most people, knows that it doesn’t have to be manslaughter to keep you up at night.” So, what keeps him up at night? “Anxiety about professional decisions, and then sometimes stuff you can’t always put your finger on. Rather than being surprised at moments when there’s professional success but personal emptiness, now it’s almost to be expected.” But equally, “who knows when you’ll turn a corner and feel really happy?”

Koenig, then, has become as attuned to his emotions as he always was to the culture around him. He riffs engagingly on how indie-rock has waned: where once hipsters had thrilled to the Strokes or, later, Animal Collective, now they’re into rap, alt-R&B and deconstructed club music, and Koenig says he was glad to be on his sabbatical when the shift happened. “For a lot of people participating in music then, that was a stressful time, an existential crisis. But a few years later, the vibe was not so much this big existential question, because to me there’d been an answer. Is rock dead? Yes. Are guitar bands relevant? Not particularly. And I enjoyed the straightforwardness of that.” He is amused and interested by the honesty of the fashion industry, and its acknowledgment of human caprice. “That industry has a straightforwardness: it’s called ‘fashion’! There’s no question about cycles. How come the person who did the same thing year-to-year is not getting the same praise as the person who changed things? Because that’s how it works. How come the person who is bringing back something from 20 years ago is getting praise? Because that’s how it works.”

His real talent is in making music that shrugs at taste. “The gods aren’t showing much favour to guitar music, but that makes playing guitar scales at home even more kind of joyful and cool to me,” he says. “It’s pretentious to say, but there’s a line from [Roman philosopher] Cato that I always liked: ‘The winning cause pleases the gods, but the losing cause pleases Cato.’ And I’m like: I feel you Cato!” Easy for a chart-topping musician to say, but you already know he knows that, too.