Anti-discrimination reforms that would prevent religious schools from excluding students on the basis of sexuality could pass their first hurdle when federal parliament resumes next week.

Greens Senator Janet Rice has told equality campaigners in Melbourne she believes support from the crossbench could push reforms to the Sex Discrimination Act over the line in the coming days.

The proposed legislation, introduced by Labor Senator Penny Wong, would prevent religious schools discriminating against students on the basis of sexual orientation, gender identity or intersex status.

“(It) looks like it’s potentially got the support of the Senate, the support of the cross-bench, that can get it through the parliament (and) that can end discrimination against students,” Senator Rice told LGBTQI equality campaigners at a rally at the State Library on Saturday.

The proposal would also have to pass the lower house.

Senator Rice wants to see it go further and is hoping to find support for her amendment to extend reforms to teachers and staff.

“We need to end all discrimination in schools, and we can do that this week,” she said.

Chris Dite told the rally that discrimination against teachers like himself hung over their heads in every interaction at work.

“What better way to force a big chunk of your employees to keep their heads down at work every single day than being able to legitimately get rid of them for no reason at all,” he said.

The exemptions don’t just have the potential to affect gay or transgender teachers and staff, but could also extend to divorcees or unmarried couples who live together, he said.

Opposition leader Bill Shorten has said Labor would introduce a separate bill protecting gay staff in the first sitting weeks of this year.

Though the major parties and crossbench have agreed on the need for reforms to prevent discrimination against students, the bill proved a contentious issue in the final sitting week of last year when agreement on how to do it coudn’t be reached.

The government has sought its own amendment to Senator Wong’s bill, wanting to include exemption to discrimination provided it is in good faith and accords with the doctrines, tenets, beliefs or teachings of a religion or creed.

-AAP