It was a fairly stunning admission to make at the beginning of a long campaign. Lyle Shelton, managing director of the Australian Christian Lobby, was asked on radio about a claim made in the first television advertisement produced since the same-sex marriage postal vote was announced.

Neil Mitchell: “Kids wearing dresses – where do you get that from?”

Shelton: “Well, that’s what Cella’s children were told at Frankston High School at the end of 2015 when the Safe Schools program was beginning to be introduced.”

Mitchell: “And did it happen?”

Shelton: “Well, I don’t know.”

I contacted the Australian Christian Lobby this week, to ask if I might speak with Shelton. I was asked to contact the Coalition For Marriage instead. This happened to me a lot. When I emailed David van Gend, president of the Australian Marriage Forum, he emailed me back to say that “as part of the team at Coalition For Marriage, I now defer to our central media contact”. When I left a message with the Catholic Bishops’ Conference, I didn’t hear from them. Instead, I got an email from the Coalition For Marriage: “They will redirect inquiries to the coalition media office, so maybe send me some questions and I’ll see if I can farm them out to a Catholic spokesperson.”

In other words, this is a tight, disciplined, on-message operation. So why wasn’t Shelton ready for Mitchell’s question?

One possible answer is that Cella White’s claims are not true. In the ad, she says: “The school told my son he could wear a dress next year if he felt like it.” The principal of Frankston High, John Albiston, told The Age this week: “We checked with all the teachers – it never happened. I have never had any complaints that we advised the boys they could wear dresses. We didn’t offer them that option.”

“If you can’t focus on old fears and stereotypes, you do your best to define marriage as a traditional, procreation-based institution that LGBTI people can’t be part of.”

This denial should not have been a surprise to anyone. In February last year, Albiston denied the claims to News Corp. He repeated the denial to The Age weeks before the ad screened. The Coalition For Marriage had time to check its facts. But when I asked if checks had been done, if they could provide me with any evidence, or any other parents with whom I might speak to substantiate White’s claim, I received no response.

Shelton did eventually call me back. He insisted Cella’s story was true, and that the Australian Christian Lobby’s Victorian director, Dan Flynn, had taken her to see Education Department officials with her complaints. But, surprisingly, he said, “Cella’s been campaigning on this for 18 months, and this is the first time the veracity of her claims has been challenged.” When I told Shelton that was not correct, and asked if he was aware of the articles in which her truthfulness had been very clearly challenged, he said he had been following Cella’s case pretty closely but hadn’t seen them.

Dawn is breaking over Sydney Harbour. We hear one of those well-oiled male voices that normally come as the credits roll on your favourite show: “We live in a country that’s been richly blessed.”

Seconds later, the image changes. Now we’re looking at a homeless man sitting on a footpath as people pass him by. The voice continues: “Right now, many of the things that have made this country great are under threat.” The camera moves quickly now, as it pans across headlines: “Push for abortion drugs to cost less than $12.” “2014 to be the year of same-sex marriage.” “Aust first euthanasia clinic in Adelaide.” “No one wins when children play with gambling apps.” By this stage, the well-oiled voice is sounding worried: “The ground is shifting, and the foundations of marriage, family and compassion are all at risk.”

This is the lead video on the Australian Christian Lobby’s YouTube site. I’ve watched it several times now, and each time I feel a small twinge when I get to this part. There are plenty of clever debating points and sharp attacks made by the lobby and others, but the video feels to me like a small glimpse of the sorrow and fear at the heart of the “No” campaign. I might disagree with many of the arguments they put forward, but when I hear that “the ground is shifting”, I don’t feel compassion because they’re wrong; I feel compassion because they’re right. Later in the video, the voice promises to roll back “decades of harmful legislation”. Decades? The world they pine for isn’t about to vanish: it vanished a long time ago.

Long-time gay rights campaigner Rodney Croome is well aware of the pace of change, and how disorienting that might be. “I remember at weddings when I was a child, all the gossip was about white dresses, and whether the bride was a virgin. I remember my grandmother being scandalised when my cousin was married in a peach dress. The point is, how quickly our understanding of marriage has changed. William and Kate cohabited before they got married, and nobody cared.”

While those campaigning against gay rights might not be happy about a changing world, they understand that’s the ground on which they must compete and have duly adapted.

“The conspicuous difference between the ‘No’ campaign now and former campaigns against gay equality”, Croome says, “is that they have steered away from any judgement about the quality or naturalness of same-sex relationships.”

Those arguments stopped about 2004, Croome says. “Almost overnight. They decided that condemning gay people wouldn’t get them anywhere anymore. Australians were not scared of gay people. There were openly gay couples in most suburban streets and country towns. If you can’t focus on old fears and stereotypes, what do you focus on? You do your best to define marriage as a traditional, procreation-based institution that LGBTI people can’t be part of.”

The residue of that argument remains as a focus on children. Andrew Hastie, the former army officer and conservative West Australian Liberal MP, summarised the position this week: “I’ll be voting no because I think marriage as it’s currently defined is both a public and societal good. It’s a special union, between a man and a woman. It’s a meeting of body and mind. It – it begins with consent and is sealed by sexual intercourse. And because the sexual union is at the heart of marriage there’s also procreative potential. And because of that fact, it’s inherently ordered towards family life. Now, the reason why the state has an interest in marriage is because of the welfare of children.”

This argument is unconvincing for a number of reasons. The first is that same-sex adoption is already legal. The second is that the vast bulk of literature suggests the outcomes for children raised by same-sex couples are as good if not better than for those raised by heterosexual couples.

And so, Croome says, the arguments have now mutated again. “We’re seeing a new argument, about the importance of gender and how ‘radical gay activists’ are supposedly trying to erase it. That is the current intellectual thrust of their campaign.”

This argument about gender is everywhere, and is an important logical step in the “No” campaign’s case. If you were wondering what the connection was between Cella White’s claims about Safe Schools and changes to marriage laws, this is it.

You might assume that same-sex marriage allows two people of the same gender to marry. But for many “No” campaigners, gender hasn’t been equalised – it’s been erased, creating a “genderless marriage”. This might sound like a silly word game. In fact, it’s crucial, providing the set-up for the next logical leap. Once you’ve removed gender from marriage, goes the argument, it’s not long until gender is obliterated altogether. As the Coalition For Marriage has it: “Removing gender from our marriage laws means removing gender from the classroom.”

People at the front line of this debate, such as Shelton, have been making arguments like this for years. In May last year, he tweeted that if genderless marriage was enshrined in law we might well be witnessing the last Mother’s Day. Last week, Tony Abbott posed a similar conundrum to 2GB’s listeners: “How, for instance, can we legitimately say no to gender fluidity programs like so-called Safe Schools if we’ve de-gendered marriage? If we’ve officially sanctioned de-gendering marriage, it’s very hard not to see de-gendering come in in so many other areas as well.”

In 2005 Tony Abbott launched a book by Sophie York, who has known Abbott for more than 20 years. York is a barrister and academic, and sought preselection for the Liberals in Brendan Nelson’s old seat of Bradfield. Abbott provided a reference. The conservative columnist Miranda Devine also backed her, writing that she was “part of a new breed of conservative feminists, generous and warm but with courage and a steely intellect … successful, normal and fun, with a fine mind, good judgement, loving family and clear moral compass”.

According to York’s website, she “contributes her time and energy” to the Institute of Public Affairs and Australians for a Constitutional Monarchy, among other groups. She is also the official spokeswoman for the Coalition For Marriage. When I put questions to the group her answers came back as boilerplate talking points.

Before becoming the coalition’s spokeswoman, York spoke on behalf of Marriage Alliance. The chief executive of Marriage Alliance is Damian Wyld, a former Liberal candidate for Florey, in South Australia. One of the alliance’s founders is Ashley Goldsworthy, a former president of the federal Liberal Party. The alliance is now part of the Coalition For Marriage, along with almost 30 other groups, including the Catholic Archdiocese of Sydney and the Greek Orthodox Archdiocese of Australia. These groups gather together under a banner that reads, “We are the silent majority.”

The “No” campaign sees silence everywhere. In 2015 York went international, telling the BBC there was a risk some people were being silenced, and therefore, “We want a safe haven for discussion.” John P. Wilson, moderator-general of the Presbyterian Church of Australia, wrote last week that many non-churchgoers “do not want to be silenced on such a socially significant matter”. Anglican rector Michael Jensen has warned of a “new censorship”.

This idea is present in the Coalition For Marriage’s chief slogan: “You can say no.” The Australian Conservatives have a Facebook ad of their own, with a similar tagline: “It’s OK to say no.”

This fear of censorship is echoed in three other prominent strands of argument. The first is that Christians are the real victims. Croome cites images of rainbow guns and rainbow nooses in anti-same-sex marriage literature. “The idea that persecution proves your righteousness has deep roots in Christianity and campaigners against marriage equality are desperate to tap into that idea by posing as victims.”

Andrew Bolt is an agnostic, but writes often about the “enemies of Christianity”. Asked to comment for this piece, he sent his response in near-biblical prose: “I know the paradigm is of yes campaigners being nice people who are fighting evil in the name of love, but from the no side it must look like an army of militants with eyes of holy fire coming for them with sharp swords in their hand and no pity in their hearts, so convinced are they that opponents are bigots and monsters.”

Bolt taps into the second strand of the “No” argument, the idea that the “No” side is the underdog: “The other side has so much money and organisational support that it put out a counter-ad in just 24 hours. There’s no way, I suspect, that the “No” camp has the resources to do the same.”

Shelton tells me that financially it is a “David and Goliath struggle”.

When I put this claim to Tiernan Brady, executive director of the Equality Campaign, he laughs, and predicts “Yes” will be massively outspent by the “colossal war chest” on the “No” side.

Whatever the case, the argument is making its way to the mainstream press. Caroline Overington wrote in The Australian this week that “No” voters “have no glamour and no money. It seems like a race between a whiz-bang Tesla and your dad’s old Falcon 500, and if Australia doesn’t have a tradition of the underdog bringing it home, I don’t know who does.”

The final strand of the censorship argument, and the most important, is that changing the marriage laws is not the end point, but the beginning of a new wave of frightening social change. This allows the “No” camp to argue issues that seem to have no direct relationship to marriage. It creates the proxy arguments on gender identity and school curricula. It also produces the false equivalencies with polygamy, bestiality and incest. It allows Eric Abetz to muse that a law to permit two men to marry might embolden another man to marry the Sydney Harbour Bridge.

Much as “genderless marriage” will usher in “gender fluidity”, the idea is that if it is hard to oppose same-sex marriage now, it will be harder soon. On his website, Bolt cites a single case of a Catholic archbishop having had to attend mediation before the Tasmanian Anti-Discrimination Commission – after a complaint that was later dropped – to ask, “Will priests be punished for refusing to conduct gay marriage ceremonies? Will defending traditional marriage be made illegal?” The fact that every bill to consider same-sex marriage has granted specific exemptions to religious groups seems not to matter. In other arguments, the concern is that once same-sex marriage is legalised religious people will feel persecuted for holding on to and exploiting these exemptions.

In my conversation with Lyle Shelton, he is keen to emphasise the threat of commercial surrogacy as well. It is, he says, inevitable once same-sex marriage becomes legal. When I put to him that I haven’t heard anyone from the “Yes” side make that case, he says, “Of course the other side don’t want to talk about it. They want everyone to think there are no consequences.”

Tiernan Brady worked on the Irish marriage referendum, which legalised same-sex marriage in the majority Catholic country. He saw similar “red herring” tactics there, but is flabbergasted at how open the “No” side is about it here. “They’re not implying this, they are directly saying this … ‘This issue is not about marriage equality.’ ”

Brady’s right. Shelton told Sky News last week: “I don’t think this debate has ever been about marriage.” I asked Shelton what he wants people to be thinking as they mark the ballot paper. He said: “We want them to be thinking about the consequences … This is a referendum on freedom of speech, freedom of religion, and what children will be taught in schools.”

In examining the arguments made, an important element can be easily overlooked: homophobia.

One “Yes” campaigner tells me that in focus groups the image that resonates most with people who are against change is men with children.

It is no accident that in 2015 the Australian Marriage Forum, which is now part of the Coalition For Marriage, ran an ad showing two men pushing a pram. The ad was broadcast on commercial television, but SBS refused to screen it. The dog-whistle was obvious: gay men cannot be trusted with children.

David van Gend, the forum’s president, is not just interested in marriage. Last year, as Queensland was considering standardising the age of consent, van Gend made a submission: “It would, for the first time in our legal history, permit older homosexual men to sodomise schoolboys with impunity … I oppose this regressive proposal, which might serve the interests of older homosexuals to lawfully obtain the object of their desire, but does not protect their schoolboy victims.”

That is the same van Gend who told me that, should I have any questions for him, I should contact the Coalition For Marriage.