The lobby's deputy director Dan Flynn said removing section 38.3 of the Sex Discrimination Act was "not something that should be sorted out in a five-minute corridor meeting", and could open up schools to unforeseen risks.

It was reported in December a number of moderate Liberal MPs would support the religious discrimination bill should the Sex Discrimination Act be amended to withdraw that clause.

Section 38.3 allows religious schools to discriminate against another person on the grounds of sexual orientation, gender identity, marital or relationship status or pregnancy.

Mr Flynn told a Senate inquiry examining the new bill that "no gay students" would be disadvantaged if it was passed, but Greens senator Janet Rice said schools already had the ability to discriminate.

"You want to keep that right ... in order to support this bill. It's to keep the right of schools to discriminate against same-sex attracted and gender-diverse students," she said.

Human Rights Law Alliance's John Steenhof tabled a number of case studies including a Christian teacher who was fired in New South Wales for refusing to teach a transgender student.

Senator Rice said Mr Steenhof was implying the "so-called religious right to misgender a child" was worth putting that child's life at risk.

"Are you aware of the level of mental distress, suicidal ideation, actual suicide of transgender and gender-diverse students who are not affirmed in their gender in their schools?" she asked.

"Not just by their classroom teacher, but by the culture of their schools?"

Mr Steenhof accused Senator Rice of trying to make the debate "emotive", adding, "I'm happy to trade stories of the deeply emotional people of faith who've been treated horribly and faced deep hostility in the workplace ... which make this bill necessary".

Meanwhile, Australia's largest women's group alliance says the prospect of the bill passing is "alarming".

Equality Rights Alliance convenor Helen Dalley-Fisher says the bill winds back protection for women and girls.

"This bill is capable of protecting sexist, racist and other discriminatory statements as long as they constitute a religious belief and are politely or benevolently expressed, no matter how serious the outcome to the person affected," she said.

"One of the biggest barriers to gender equality is tackling unconscious bias and discriminatory norms and cultures."

The religious discrimination bill is designed to protect those expressing religious beliefs as long as it isn't done maliciously or in ways that vilify, threaten or intimidate others.

Religious schools and organisations could also preference hiring people of the same faith.

Australian Associated Press