Two cross-party parliamentary inquiries into the coalition's religious discrimination bill have recommended it be passed, albeit with changes to address concerns about key pillars of the legislation.

The changes include a clause designed to protect people who express religious beliefs, even if they are offensive, from discrimination claims, as well as provisions overriding state laws limiting faith-based hiring.

With these caveats, the legal and constitutional affairs committee recommended the bill it saw as "a necessary addition to Australia's anti-discrimination laws" be passed.

There were calls for outdated provisions in section 38 of the Sex Discrimination Act, letting religious schools discriminate on groups of sexuality and gender identity, to be removed before the bill was dealt with.

Support for the proposed laws came on Friday as protests were held in Brisbane against a Christian school that had proposed student enrolment contracts that included sexuality and gender clauses.

Brisbane's Citipointe Christian College issued contracts to parents last week stating "the college will only enrol the student on the basis of the gender that corresponds to their biological sex".

The school's contract also likened homosexuality to incest, pedophilia and bestiality.

The proposed contracts had drawn widespread condemnation, leading to the school withdrawing the measure on Thursday.

The school's principal later apologised over the incident and to LGBT students, stating he regretted that some students felt they were being discriminated against because of their sexuality or gender identity.

Citipointe Christian College principal Brian Mulheran on Friday night said he had decided to "stand aside and take extended leave in order to reflect on what has transpired and provide the College community time to heal".

The recent situation at Citipointe had amplified concerns held by LGBTIQ+ advocates about the potential ramifications of the religious discrimination laws.

Back in Canberra, a separate bipartisan human rights inquiry into the laws concluded most religious organisations would want to hire based on ability, not faith.

At the same time, that committee thought the bill as a whole represented "a sensible and balanced approach" to protecting religious freedom.

It called for the laws to be passed subject to 11 other recommended tweaks.

Equality Australia criticised both inquiries for failing to fix problems with the laws that would unwind hard-won protections.

"After three years of trying to solve a problem of the government's making, the committees were left with the pieces of a broken and friendless bill," chief executive Anna Brown said.

"It's no wonder they failed to find a way to fix it. It is time to throw out this failed, experimental bill."

Just.Equal Australia said the major parties had glossed over key problems and ignored concerns held by the majority of Australians.

Labor, which has treaded carefully in an attempt to keep religious voters onside, pointed to a litany of issues with the way the government had gone about the laws.

It said there was a consensus, including from the attorney-general's department and Prime Minister Scott Morrison, that the package required amendments.

Australian Associated Press