Roxanne Tickle is suing Giggle for Girls after having her access to the app revoked in September 2021.
Supporters for both sides gathered outside the Federal Court near Sydney's Martin Place and protested within metres of each other.
As the proceedings got under way, Justice Robert Bromwich said the court would not tolerate any "intimidation or harassment" either within the courtroom or outside it.
A judge has warned supporters on both sides of the case. (Bianca De Marchi/AAP PHOTOS)
"I appreciate that the issues from this case give rise to strongly held views and emotions," he said.
Some members of the public had shown they were "unable or unwilling to tolerate the existence of any view contrary to their own", Justice Bromwich added.
Ms Tickle was issued a birth certificate stating she was female a year after undergoing gender-affirming surgery in October 2019.
But Giggle for Girls, which cites itself as "made for women by women", blocked her after considering her male.
Ms Tickle's lawyer, Georgina Costello, told the court in her opening statement that "gender is not merely a biological question, it is partly social and partly psychological".
"Ms Tickle was assigned male gender at birth but she has changed to being a woman and that fact is clear in this case," she said.
Transgender rights supporters outside court. (Bianca De Marchi/AAP PHOTOS)
Giggle for Girls had illegally discriminated against Ms Tickle on the grounds of her gender identity, Ms Costello argued.
In a statement filed with the Australian Human Rights Commission in December 2021, before the Federal Court case was launched, Ms Tickle outlined the alleged discrimination.
"I believe that I am being discriminated against by being provided with extremely limited functionality of a smartphone app by the app provider compared to that of other users because I am a transgender woman," Ms Tickle wrote.
"I am legally permitted to identify as female."
The hearing continues.
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