As it stands, Australia allows people to mark their gender 'X' on documents such as passports.
Australians can also apply for a revised birth certificate and a gender recognition certificate on the condition that a person provides a letter from medical professional or psychologist, or even the provision that applicants undergo a sex affirmation procedure.
In some states the declaration to be legally recognised as a non-specific gender is only allowed for people who have undergone surgery.
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Transgender Victoria Executive Director Sally Goldner said these barriers were a double-standard.
"It comes down to this idea that trans people have to go through an extra layer of proof - there might be something inaccurate or, god forbid, fraudulent about us," she told SBS.
"No, we are who we are. The same as people whose gender-identity meet expectations given their gender at birth."
The call comes as Canada's Prime Minister Justin Trudeau said his country was exploring the use of gender-neutral options on identity cards.
Mr Trudeau said Canada would look to countries such as Australia for guidance, as it considers implementing laws where people are eligible to put male, female or X for gender neutral on drivers licences.
This comes a week after the Canadian province of Ontario announced it would employ these measures.
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Also backing the call for greater flexibility is Sydney resident, Norrie, who won a High Court battle in NSW to be legally recognised as neither male or female.
"Any person who is intersex of non-binary as I am, we get told we can't get married at all, because the law says marriage is between a man or a woman," Norrie said.
"So then they put pressure to say well give us paperwork to saying you're one thing or the other. I want everyone to have equal rights and not have to say well I'm not normal gender A not normal gender B."
Organisation Intersex International Australia told SBS it would like to see the removal of sex or gender markers on official documents, just like with race or religion.
