Labor backs the federal government's controversial bill to shield religious Australians from existing discrimination laws, albeit with caveats and changes.
Two cross-party parliamentary inquiries into the religious discrimination bill recommend it be passed. But both reports call for changes.
A constitutional affairs committee wants two points revisited, including concerns over a clause to protect religious expressions of belief, even if they are offensive, and the bill's ability to override state laws limiting faith-based hiring.
Should those concerns be addressed, the committee recommends the bill be passed.
A separate human rights inquiry has made 12 recommendations on which support for the law is predicated.
"The Labor members of the human rights committee believe it is totally appropriate - and should not be at all controversial - for a modern Australian parliament to legislate to protect people of faith from discrimination," Labor MPs and senators said in the report.
They noted concerns about statements of belief and the law's ability to override the Victorian government's laws restricting when religious schools can preference hiring people of the same faith.
Labor supported the idea of faith-based hiring in schools, but criticised the federal government for not consulting with states.
The opposition also questioned whether states could pass new laws simply override the federal clause.
Labor supported protections for statements of belief but criticised the lack of "proper, public and bipartisan" consultation.
"Labor members believe that the national parliament has a role to play in reassuring people of faith that the mere expression of what the bill describes as 'moderately expressed religious view' do not contravene any Australian law," the opposition politicians said.
"However, we also believe that this can and should be done in a way that does not remove protections that already exist in the law to protect Australians from other forms of discrimination, or lead to the perception that they have been removed."
Prime Minister Scott Morrison has insisted his government will stop church schools excluding same-sex attracted and gender diverse students alongside the religious discrimination bill.
Moderate Liberals had predicated their support for the bill on changes to section 38 of the Sex Discrimination Act letting religious schools discriminate on grounds including sexuality and gender identity.
But Mr Morrison's commitment is at odds with conservative senator and Assistant Attorney-General, Amanda Stoker, who wants to wait until the religious discrimination bill is finalised.
"It's important that the two integrate well because if you change one without knowing the final form of the Religious Discrimination Act that emerges from the Senate, you could end up actually creating problems rather than solutions," Senator Stoker told ABC radio.
"We are trying to make it (Sex Discrimination Act changes) happen and I expect we will make it happen but I'm not going to sign it in blood."
The issue, which has its roots in conservative opposition to same-sex marriage, has again come to a head over a Brisbane Christian school's abandoned attempt to enforce a sexuality and gender contract.
Citipointe Christian College withdrew the contract stating it would only enrol students "on the basis of the gender that corresponds to their biological sex".
It also claimed same-sex attraction was a sin and compared it to bestiality, incest and paedophilia.
