The Book of Mormon, the much-applauded musical from the creators of South Park, officially opened in London last week – and like the grinning, clean-cut missionaries whose story it relates, it's been getting some baffled reactions from the locals. Well, the ones who work as professional theatre critics, anyway. I saw it on Broadway last spring, and can't recall a more purely hilarious and heart-warming evening in years. But the Telegraph's Charles Spencer found it "hard to warm to", "decadent" and "self-indulgent". My colleague Michael Billington, though deeming it "perfectly pleasant", also called it "essentially a safe, conservative show for middle America", awarding three stars out of five. Quentin Letts, of the Mail, called it "cowardly, coarse, cynical" and "worth avoiding"; in the Times, Libby Purves found it "morally null" and even "pretty racist".

Not every British critic was so negative: if you want to know my feelings about the musical, just read Euan Ferguson's Observer review, its ink practically smudged from tears of laughter. Even so, this is a show that won nine Tony awards, and which the New York Times – leading the near-unanimous praise from US critics – called "something like a miracle". What in the name of Joseph Smith is going on?

The first strange thing about this difference of opinion: you'd have thought it might have been the other way around. Surely, it's the Brits who'd be belly-laughing at the idea of two deluded Yanks leaving their Salt Lake City comfort zone to impose their preposterous religion on sceptical rural Ugandans? And oughtn't it to be the prudish, super-religious Americans pursing their lips at the show's song-and-dance centrepiece, a parody of The Lion King, with its multiple obscene references about what the embattled Ugandan villagers would like to do to God?

The second curiosity is how much the unimpressed Brits disagree with each other. Is The Book of Mormon conservative, as Billington argues, because it allows that there might be some upsides to religious belief? (The show's missionaries are deluded and emotionally repressed, but by the end, you can't help liking them.) Or does it consist of vicious "liberal … sneers" against Mormons, as Letts claims? (Mormons themselves disagree, actually, but never mind.)

Letts even trots out that laziest of criticisms, never far away whenever Christians are being satirised:

"If you want to attack a religious group, why not militant Islam?"

Ah, yes: Trey Parker and Matt Stone, dogmatic line-toeing liberals, who'd never risk offending the PC left. Quentin Letts, please take the rest of the week off, and spend it catching up on South Park and Team America: World Police.

But all of this points towards the great value of Parker and Stone's comedy, which elevates "take no prisoners" to the status of an ethical principle. Just as you're getting comfortable laughing at others from the safe haven of your smugness, you look down to find nothing but air. Their special talent is to do this without succumbing to hollow nihilism, thanks mainly to the sincerity with which they appreciate old-fashioned showtunes and scatological humour. You come away from The Book of Mormon – if you're more like me than Letts, anyhow – with the sense that religious people can be ridiculous, but not in ways to which the non-religious are necessarily immune. And that, besides, even ridiculous people can have non-ridiculous qualities; they need not provoke only our monotone disdain.

If you'll allow a vast cultural generalisation from the perspective of a British person living in the United States: comfort with this kind of complexity, I suspect, is something at which Americans are peculiarly good. Perhaps this explains the transatlantic disagreement. You can't really function in America – you can't even turn on the television – without a high tolerance threshold for people with absurd beliefs. Many of them deserve condemnation, of course; this isn't an argument for passively tolerating bigotry. But if you can't countenance the idea that even these people might have some redeeming features as humans, too, you'll find yourself ceaselessly embattled, enraged and exhausted.

Far better, The Book of Mormon seems to say, to locate that vantage-point from which you can laugh at others' absurdities; laugh at your own; engage in pointed, angry satire when you need to; make running jokes about scrotums; and still maintain a certain cracked and off-kilter faith in humanity. "You can't be Swift and Pollyanna at the same time," Billington argues in his review. But I'd respectfully disagree: sometimes, it's the only way to stay sane.