Campaigners are setting their sights on New South Wales, Western Australia and Queensland after Victoria passed a new law to allow trans and gender-diverse people to change their recorded sex on their birth certificates on Tuesday, following a heated debate.

Despite some reservations from independent members of parliament, the Victorian legislative council overwhelmingly voted in favour of the bill, 26 to 14 on Tuesday night.

The Liberals opposed the legislation, with one MP claiming it would lead to women and girls being molested. Supporters of the bill denounced such rhetoric as desperate, nonsensical and “extremely hurtful”.

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The bill requires the person making the application to make a statutory declaration when nominating the sex to be recorded, and must include a statement from an adult who has known them for 12 months or more who believes the application is being made in good faith and supports the change.

The legislation passed the legislative council without amendment after a majority of independent members sided with the government to pass the bill.

The new law came after what MPs described as some of the most intense campaigning in the state, with MPs saying they had received hundreds of emails from those in favour and those opposed to the legislation.

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A new women’s group, Victorian Women’s Guild, was spawned in opposition to the legislation on the grounds of the potential impact it would have on women-only spaces, while Equality Australia responded with an open letter of over 1,000 feminists supporting the change.

Legal director of Equality Australia, Lee Carnie, told Guardian Australia that other states that had yet to change the law would now be the focus for campaigners.

“WA, Queensland and NSW are next in line for birth certificate reform,” she said. “Equality Australia will be working with trans advocates from across those states for fair birth certificates.”

Liberals opposed the legislation, with the conservative Liberal MP Bernie Finn stating it would put his daughters in danger . He said the legislation was an “attack on our society”.

“There are two genders. Of the two genders, there is the male – there is homosexual inclination and various paedophilic inclinations, there are a whole range of inclinations, and we could go on with that for quite some time. But in terms of gender, there are only two genders: male and female,” he said.

“I do not want a man who claims to be a woman to get a birth certificate which says that he is a woman. I do not want him to get that birth certificate and use that as a way to molest women, to molest young girls, as some inevitably will.”

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The Animal Justice party MP David Meddick rebuked Finn’s claim.

“Throughout history, in many cultures, various genders have been recognised and simply been part of the fabric of society, not pointed at, discriminated against or marginalised in any way. Life – human life – was observed and accepted in all its wondrous diversity in these communities, but not in all,” he said.

Just three out of the 10 crossbench members voted with the Liberals: two Justice party members, Tania Maxwell and Stuart Grimley, and the Shooters and Fishers MP Jeff Bourman.

Grimley described the legislation as “the most difficult process” he had taken in his time in parliament. He said he could not support the legislation because of concerns he had about men entering women’s spaces, but said he still believed people had the right to change their birth certificates.

Liberal Democrat MPs, who supported the legislation, pushed for an amendment to remove the recording of sex from birth certificates entirely on the grounds that “what your gender is and what is inside your underwear is none of the government’s business” but it was defeated after the government opposed on the grounds it would create unintended consequences, including around government data collection.

It was the second time the Victorian Labor government had attempted to change birth certificate legislation, after the legislation was defeated by one vote in 2016. Transgender Victoria spokesperson Brenda Appleton said that the favourable speeches in the council on Tuesday night were “amazing” and helped heal the damage from the debate three years ago.

“It is important that we can all [have] documents which reflect who we are and enable us to get on with our lives with pride rather than hiding in the closet,” she said.

The Greens Victorian leader, Samantha Ratnam, noted some of the debate had been “extremely hurtful” for the trans and gender diverse community.

“Those spewing hate have lost, and they know they have lost. Like all gains for human rights over the centuries, we are witnessing the last gasp of those who would deny such rights, which is why their rhetoric makes no sense and sounds so desperate.”