Faith-based schools will still have the right to discriminate against gay students into 2019 after the coalition and Labor failed to reach a deal on law changes.
Even though the government and opposition both agree the largely redundant legal right for religious schools to discriminate should be removed, they cannot agree on the wording of legislation.
Labor objects to the government's inclusion of a clause allowing schools to teach in accordance with their religious beliefs, believing it broadens the ground for discrimination.
But the government says the bill "looks after kids", while preserving religious freedom.
There is no evidence gay children are discriminated against by religious schools which have indicated they don't use the right to do so.
But the issue arose following a leaked religious freedom review report which raised fears about potential discrimination and Prime Minister Scott Morrison vowed to have it resolved by the end of the year.
Minutes after a bill was postponed in the Senate on Wednesday due to a lack of agreement, Mr Morrison put forward a three-pronged proposal which he said could be dealt with as a private member's bill and put to a conscience vote.
The bill would remove the ability to discriminate against students based on gender or sexual orientation or relationship status or pregnancy.
It would also clarify that in deciding whether a school rule was "reasonable", the Human Rights Commission and courts should take into account the religious nature of the school and whether it considered the best interests of the child.
Thirdly, nothing in the law would prevent a religious school teaching in accordance with their own religious beliefs.
"This is a good bill. It actually does what I think Australians would expect us to do - look after kids for who they are, but also ensure that in this country, religious freedom still means something," Mr Morrison told reporters.
But Labor deputy leader Tanya Plibersek said the government had complicated every effort from the opposition for progress, just as it did with marriage equality.
"Why are we contorting ourselves?" Ms Plibersek asked reporters.
"The solution is to remove the exemptions from the Sex Discrimination Act that allow discrimination against children. It is simple."
Labor has legal advice that says the proposed changes go too far, especially the new clause allowing schools to teach "in good faith" their doctrines, tenets or beliefs.
"For example, a teacher or school could provide inferior instruction to a student on the basis of the student's sex, sexual orientation, gender identity or intersex status or, indeed, exclude that student from instruction entirely," Mark Gibian SC said in advice to Labor.
The advice also says Labor's amendments will not prohibit or constrain religious schools "teaching of scripture".
Attorney-General Christian Porter said religious leaders and schools believed Labor's approach would limit the bounds of faith-based teaching not only in schools but churches, synagogues, mosques and temples.
"Bill Shorten should be ashamed, and anyone concerned about these exemptions need look no further than to the fact that the Labor Party, which put them there in the first place, will not allow a conscience vote to have them removed," he said.