Malcolm Turnbull has thrown his support behind the “yes” vote in the same-sex marriage debate, telling like-minded Liberals and Nationals it is a question of “fairness”.

Addressing the New South Wales Liberals and Nationals for Yes campaign launch in Sydney on Sunday morning, Turnbull said this change had already happened in many countries around the world.

“In any one of those nations has the sky fallen in, has life as we know it ground to a halt, has traditional marriage been undermined and the answer is plainly no,” he said.

‘The threat to marriage is not gay couples’: Malcolm Turnbull at the New South Wales Liberals and Nationals for Yes campaign launch. Photograph: Paul Miller/AAP

Speaking at a packed Sydney rally on Sunday afternoon, the opposition leader, Bill Shorten, said that he was determined to see Australia allow gay couples to marry. He said he expected the yes vote to prevail in the postal survey but not because of politicians.

“It will be because Australia has said it’s time to may make marriage equality a reality,” Shorten said. “I’m very optimistic.”

Earlier on Sunday, Turnbull was joined by New South Wales Liberals including the former premiers Barry O’Farrell and Nick Greiner; the former NSW Coalition leaders Kerry Chikarovski, Peter Debnam and John Brogden; as well as Sydney city councillor Christine Forster, who is the sister of the former prime minister Tony Abbott.

The room of about 130 people, mostly young Liberals and Nationals, applauded when Forster took to the podium.

Forster said she had already set a date for her marriage to her partner, Virginia Edwards – 2 February 2018. Forster said they set that date with the plan to get married in the British consulate.

“I do not trust our federal leaders to get this done,” she said of her thinking at the time.

But she said if the “yes” case wins the postal vote and the federal parliament makes the change, she will get married under Australian law.

Bill Shorten at the rally in support of marriage equality in Sydney. Photograph: Paul Miller/AAP

“That is what we want to do,” she said. “And that is what so many other Australians want to do.”

Greiner spoke of lesbian family members who were unable to marry while Brogden spoke of gay neighbours who played in important role in his childhood. Debnam spoke of the realisation he and his wife had when they considered what would happen if one of their children or grandchildren was gay and wanted to marry.

All of the speakers described marriage equality as a fundamentally conservative value – one that they wanted to extend to all loving couples.

“This is not a cause that divides along party political lines,” Turnbull said.

He said he was “utterly unpersuaded” by the idea that his 38-year-long marriage to his wife, Lucy, could be undermined by gay couples.

“The threat to marriage is not gay couples, it is a lack of loving commitment,” he said. “Whether it is found in the form of neglect, indifference, cruelty or adultery.

“If the threat to marriage today is lack of commitment then surely other couples making and maintaining a commitment sets a good rather than a bad example.”

Rallies in support of same-sex marriage were being held in various cities on Sunday afternoon.

At church with Christians For Marriage Equality. They're going to today's Sydney #marriageequaility rally #abc730 pic.twitter.com/5gK1GULWSv — Julia Holman (@JulesHolman) September 10, 2017

Sending 😘🌈💕✨🦄 to the fabulous LGBTIQ folks and allies in Sydney rallying for marriage equality. The message is simple: #VoteYES for us all. pic.twitter.com/u5n34vXmUj — Senthorun Raj (@senthorun) September 10, 2017

Before addressing the rally in Sydney, Shorten urged marriage equality activists to turn their disappointment the survey was going ahead into a determination to win it.

“We have a chance to not only make marriage equality a reality in this country, we have a chance for Australia to send a message to the world that Australia is a modern country, we are a country which believes that all people are equal,” he told reporters.

“We’ve got one last mountain to climb to make marriage equality a reality – let’s climb it together.”

In Brisbane, same-sex marriage campaigners responded to a religious counter-protest with an impromptu rendition of Gloria Gaynor’s I Will Survive.

A chorus of boos from the rainbow-attired crowd rang out in a packed Queens Gardens when the opposing group arrived bearing signs reading: “The wicked shall be turned into hell.”

Police at Sunday’s event stood between the two sides but tensions dissipated after the gay marriage advocates completed a chorus of the popular 1970s song.

The marriage equality advocate and federal MP Tim Wilson told supporters at the launch of the Victorian Liberals and Nationals for Yes campaign launch in Melbourne on Sunday that a yes vote aligned with party values.

“This postal survey is an opportunity to show the traditional Liberal values about commitment and responsibility to the country and we urge every single Liberal and National voter across this nation to vote for a change in the law,” the member for Goldstein said.

The postal survey forms with the question “Should the law be changed to allow same-sex couples to marry?” will be mailed to voters from this week. They will have the option to tick a “yes” or “no” box.

The result of the survey will be announced on 15 November, followed by a vote in parliament on a private member’s bill if there is a majority “yes” result.

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• Australian Associated Press contributed to this report