When Tim Minchin – actor, comedian, confirmed atheist – decided to take his comedy to America's Bible belt, we were concerned he might be burnt at the stake. Here, he describes what happened next…

The hire car guy at the airport in Phoenix, Arizona, tells us there are no "standard" cars left, then suggests that for an extra 10 bucks we might want to upgrade to a Camaro – a muscular Mustang-wannabe into which I have to fold myself like a circus clown. Grizzly, my tour manager (he has a thick beard and the surname of Adams, and has taken to my nickname like a bear to dancing), starts up the engine and we are amused to hear it roar like my VW Golf. I'm not going to use this flashy-body-but-nothing-under-the-hood vehicle as a metaphor for American culture, but it's tempting. Not that I give a shit about cars, but I do quite like lazy symbolism.

Speaking of which, looking out of the plane window as we flew in, I'd been struck by the incredible stubbornness required to build such a huge city in the middle of the desert – the gridded oasis appearing to me as both a triumph over nature and a childishly futile act of defiance, like firing a toothpick at a dragon. Long before Oprah started peddling her popcorn psychology, these people were scarily optimistic.

We drive out of the airport past the compulsory orgy of American flags, which despite their quiet fluttering still manage to scream: YOU'RE IN AMERICA! YOU'RE IN AMERICA! YOU'RE IN AMERICA!

Where am I?

Oh, yeah. Thanks.

Whenever a friend or fan finds out I've started touring the States, there is an inevitable raising of the eyebrows (or eyebrow, if they are blessed with that most enviable of talents). There are two reasons behind such browular elevations, the first of which is born of comedy snobbery: Brits and Aussies are very fond of saying that Americans "don't get irony". This is absurd; if anything, they don't get absurdity, which the Brits and the Irish probably "get" better than anyone else. Apart from that, I have observed a surprising consistency in what makes people laugh, notwithstanding geography-specific subject matter, which I avoid. (The only other cultural-comic quirks I have observed are that the English really like camp men making thinly veiled bum-sex double entendres, and Australians love swearing. We think it's fucking hilarious.)

The second thing that concerns people about me touring the US is that they fear my penchant for jaunty-but-vehement criticism of religion will at best result in empty auditoriums, and at worst get me shot. But the perception that the country is packed wall-to-wall with Christian fundies is as specious as the irony myth. There is no doubt that many Americans have what seems to be a near-erotic relationship with the two-millennium-dead Middle-Eastern Jewish magician-preacher we call Jesus. But there are frickin' loads of people in America, and even if the percentage of the population that is not religious is only 10% (it's a much greater number, surely), then there are still 33 million potential ticket-buyers.

If there is a problem with my US shows, it is the opposite: unlike in the UK and Australia where my audiences are very mixed, here in the US I am preaching – as it were – to a congregation that is 99% fully frocked-up choir. One shouldn't be surprised, of course – nothing increases passion for a philosophy more than living surrounded by people who do not share it. In DC a couple of months ago, I met husband-and-wife biology teachers who had flown up from Kentucky to see my show, and the fella started to cry as he told me how their families don't talk to them any more since they started speaking out about the importance of science in their small Southern town.

My first forays into the US live scene were in proper liberal cities. In Portland I was offered cocaine, in Seattle a threesome, in LA cocaine and a threesome. (That I refuse such offers is by the by; it's the thought that counts.) A guy tried to pick me up in a New York cabaret bar, which was a great relief as I've always found it upsetting that dudes don't find me attractive. These were my kind of towns… but I assumed my ability to draw a crowd would correlate to my proximity to the coast.

And yet here I am in Mesa, Arizona, in a beautiful, new 750-seat theatre, and – just like in St Louis and Minneapolis and Atlanta and Boulder and Austin – here comes my audience: a familiar motley crew of teens and grey-hairs, scientists and English teachers, students and statisticians, skinny, shy men in uncool jeans and gloriously big-boobed, tattooed S&M-ish women. Smart, quirky, different and – overwhelmingly, passionately – Godless.

A little after 8pm, I walk cautiously on to the stage and the crowd goes completely nuts, as is the custom in this culture of über-affirmation. As I sit they spontaneously start singing "Happy Birthday". This is weird, but much less weird than it would be on any other day of the year (it is, actually, my birthday). After the gig I venture out into the theatre's foyer to see if anyone has hung around for an autograph and, sure enough, there's a big group of patient Arizonans waiting with merch and cameras.

I recognise among them a sexy, 6ft, 40-ish blonde woman who has previously flown to see me in LA and Portland. She is wearing a belt that has a scrolling LED screen where the buckle should be. I spot it halfway through its scroll and think it says "HEIST" (a brand name, perhaps?) It scrolls again and I realise I'm mistaken. Mesa is serious Mormon country and she has accessorised with a flashing sign nestled against her pubic bone declaring: ATHEIST. Ya gotta admire the balls. Oh, and she'd brought her husband and four young children with her. I have a song in my show that utilises the word "fuck" 160 times in two minutes. Liberal? Eat your heart out San Francisco.

I, on the other hand, don't tend to walk around with glowing atheist belt buckles. I've been atheist since I became aware of the term, but my material is not all about religion – not by a long shot – and when I do address the topic it is to point out where religiosity meets discrimination. Many comics write about what makes them angry, or, at least, what they observe in the world that is at odds with how they feel it ought to be. This is the case when Seinfeld talks about muffins or McIntyre talks about Argos (brilliantly, I hasten to add). I just happen to be less preoccupied by parking spots and soup nazis, and more by homophobes and creationists. Here in America it seems to be the God stuff that people are coming to see.

I don't get to bed until 1.30am, and am up at half-six in the morning for a flight to Texas. No time to Skype my kids, which is depressing – a digital dad is surely better than a non-dad – but we need to get to the venue early today, as I'm worried about the piano. Usually we sort out pianos well in advance, but we had a bit of trouble with our planned hire in Dallas. Three days ago, Grizzly received an email from the company who had been booked to supply us with a lovely Baldwin. The subject heading was "CANCEL !!!!!!!!!!" (yep, 10 exclamation marks), and the body of the email read:

"I need to decline after watching that insane Tim Minchin. What a God-hater.

So sorry, please cancel the Entire Event In Dallas. Go back to Australia we do not appreciate Tim Minchin in TX.

WE ARE NOT DELIVERING THE GRAND PIANO!!! NOT FOR 1 MILLION $ HA HA HA.

You probably agree. Find a better comedian (not a demon).

Love in Christ,"

And there they signed off.

It is clear from the use of caps that the writer of this email is a bit of a goose, and I am certainly not suggesting he is a typical Christian, nor a typical citizen of Dallas. But it's amusing that it happened to be here in Texas that I came across my first proper religious nut. The governor of this fine state is Rick Perry, the Republican presidential frontrunner and a genuine capital-C Conservative – anti-socialist, pro-guns, anti-gay… and yet quaintly enamoured of the aforementioned long-dead Semitic pacifist who said wealth was bad and that you should love everybody. (Perry is also a global-warming denialist – once you reject evidence as a source of knowledge, you don't gotta believe nothin' you don't like.)

As we drive from airport to theatre, the Dallas sky is vertiginous and blindingly blue and the skyscrapers downtown shimmer with Southern confidence, the kind of self-assurance that also means its citizens can get away with a 10-gallon hat and a moustache without looking like a Village Person.

The theatre is a gorgeous Art Deco cinema converted into a concert venue, and the people are lovely… but that's where the positives end. The instrument brought in to replace God's personal piano is crap, and there's a lovely, shy, but incompetent kid behind the mixing desk. My concerns about security are replaced by frustrations with the frequency of screaming frequencies in crackling fold-back wedges. If I had a religion, its deity would be Audysseus, the sound God, and He would be a vengeful god, dishing out eternal damnation to people with cheap stage monitors.

Happily, I get to leave Grizzly to solve my problems, as a local photographer – hired to take up the challenge of capturing a palatable angle of my ridiculous head – whisks me away to downtown Dallas. Danny has a Texan drawl, but otherwise fails to fit the cliché. His car is shockingly normal-sized and he starts a diatribe against homophobia that segues happily into a searingly negative review of his governor. He tells me Perry recently organised a "prayer rally" where 30,000 Texans gathered to ask God for rain. Apart from the fact that government promotion and expenditure for such an event surely constitutes a contravention of America's overtly secular constitution, it also failed to work: more drought and terrible fires appear to have been God's chuckling response.

Later in the evening, struggling like DJ Dante through acoustic hell, I get the giggles during my song "Thank You God (For Fixing The Cataracts of Sam's Mum)" – a ditty that pokes fun at the megalomaniacal idea that an omnipotent being might have his attention diverted by the plight of a middle-class woman with minor ocular issues. Here in Texas, where it's perfectly normal to pray before every football match, board meeting and exam, and where the governor will happily organise mass rain-dances while ignoring climate data, it feels like the song has found its spiritual home.

The audience response tonight is lovely, and despite (or because of) the polemical tone of much of my material, the room fizzes with positivity. As an encore, I play my sentimental Christmas song and then get them to sing along to a Leonard Cohen's "Hallelujah". I turn off my microphone, and they break into harmonies without prompting. It's beautiful.

After an hour signing stuff for the weird and wonderful heathens of Texas, Grizzly and I walk out of the theatre into the previously dusty Dallas street to find it is absolutely pouring with rain.

Tim Minchin & the Heritage Orchestra Live at the Royal Albert Hall is available on DVD from 14 November (timminchin.com). Matilda: The Musical opens at the Cambridge Theatre, London on 24 November