You could, if you wished, infer a great deal from the stage set of Taylor Swift’s Reputation tour. Not since the British Herpetological Society held their AGM at a local museum has Manchester seen quite so many snakes gathered together on one stage. There are films of snakes. There are films of Taylor Swift wearing clothes covered in snakes. There is a platform covered in snakes upon which dancers recline, three different giant inflatable snakes with illuminated eyes that rear up from the stages dotted around the Etihad Stadium. There is a huge skeleton of a snake attached to a wire, on which Swift flies across the arena, singing Bad Blood.

One interpretation would be that all this reflects the worldview frequently presented on the 2017 album after which the tour is named. Therein Swift depicts herself as constantly assailed by various reptilian forces, a panoply of “liars” and “big enemies”, former friends and lovers, internet commentators, gossip mag journalists: infamy, infamy, they’ve all got it infamy, as Kenneth Williams once cried. Certainly, Swift’s public image seems to be the theme of the show, which opens with the sound of Joan Jett’s punky 1980 hit Bad Reputation, concludes with the screens displaying a message about the death of the singer’s reputation and in between features routines in which dancers recoil from Swift as if she’s got a contagious disease and projections of news headlines bemoaning her awfulness.

You can perhaps forgive her for feeling embattled. In an online world where censure is hot currency, she’s been accused in recent months of everything from encouraging the attentions of the “alt-right” – some sections of which have adopted her as an icon of Aryan femininity – to making perplexing demands of her gig-going fans: a report on an Irish website this week claimed that, among the items prohibited at her forthcoming Dublin shows were not just the usual illegal substances and glass bottles, but “lightsabers” and “tridents”, the latter clearly a serious blow for any classical sea gods who were planning on attending. On record, her sourness about her transformation from America’s sweetheart to an all-purpose piñata, however understandable, can occasionally become a bit much. On Reputation’s weaker moments, it felt like it was overwhelming her undoubted talents as a songwriter – but onstage, it really works: there’s an evident sense of humour and absurdity about blowing up both the controversies she’s created and her response into such a preposterous, grand spectacle. Look What You Made Me Do, by her high standards a weak single, gains a thunderous heft performed live; played for laughs, the spectacularly chippy This Is Why We Can’t Have Nice Things takes on a certain charm.

For all the grandiosity of the production, it never feels like Swift herself is dwarfed. A product of Nashville before mainstream pop success came calling, she’s as capable of holding the audience alone, with an acoustic guitar or a piano, as she is aided by high-definition video screens and inflatables. The setlist also serves as a potent reminder of her abilities as a writer. If the EDM-influenced fizz of Reputation can sometimes seem boilerplate – Dress isn’t a bad song, but it could be by anyone – the Bruce Springsteen-esque Love Story is the kind of blend of heartland American rock and unashamed commerciality that only Swift could pull off successfully, while Shake It Off and Bad Blood are just exceptional examples of pop songwriting craft. In fact, as stadium-sized pop shows go, it’s something of a triumph: for a woman who keeps complaining that she’s damaged goods, she seems to be doing just fine.