Scott Morrison’s proposed new religious discrimination bill could backfire against the controversial chaplains programs in public schools and the military, an expert has warned.

Associate professor Luke Beck, an expert in the separation of church and state, has welcomed the proposal to prevent discrimination on the grounds of religion but noted it would provide an additional avenue to challenge the chaplains programs.

The head of the religious freedom review, Phillip Ruddock, has conceded the panel did not find “a lot of evidence” of discrimination against religious people, despite the prime minister saying a new law was required because religious people feel the “walls … closing in on them”.

In its response to the Ruddock review, the government announced it would introduce a bill to render it unlawful to discriminate on the basis of a person’s religious belief or activity, including that he or she does not hold a religious belief.

Programs to place religious chaplains in public schools and the military have both been the subject of complaints to the Australian Human Rights Commission, the body that would house the new religious freedom commissioner to oversee religious discrimination complaints.

Beck told Guardian Australia that if the bill makes it “illegal to discriminate in employment on the grounds of religious belief, that would give rise to questions of whether the hiring practices of the military and school chaplains programs are lawful”.

Both programs require chaplains to be from recognised organised religions, and the positions cannot be filled by secular pastoral care workers with no religious beliefs.

“One of the worst offenders when it comes to discriminating on the grounds of religion is the federal government itself,” Beck said.

“They are the ones that have the school chaplains program which effectively limits jobs in public schools [to religious people] … usually only Christians are able to get those jobs.”

Beck said the chaplains programs can already be challenged under the Fair Work Act, but the passage of a Religious Discrimination Act would create a new avenue to complain to the AHRC and then to take a case to the federal court if it did not settle in conciliation.

Meredith Doig, the president of the Rationalist Society of Australia, said her organisation would seek to use the new law to challenge the legality of refusing to hire secular chaplains in schools.

On Friday Ruddock told Radio National the panel “didn’t find a lot of evidence of actual material discrimination that would be of concern” against religious people but said Australia had signed up to international law that recognised people should not be discriminated against for their religion.

He conceded the panel had not recommended a new religious freedom commissioner but said it would “not be adverse to it”.

Shadow attorney general Mark Dreyfus told ABC News Breakfast Labor will consider a religious discrimination act because it was opposed to “all form of discrimination”.

But he said religious freedom was already a hallmark of Australian society and “even the Ruddock review did not identify any real threat to religious freedom”.

The school chaplains program received a four-year $247m funding extension in the 2018 budget.

In April the Rationalist Society asked the AHRC to review whether the school chaplains program infringed freedom of religion, but it refused, citing the ongoing Ruddock review process.

The school chaplains program is currently the subject of a case in the Victorian Civil and Administrative Tribunal arguing it is discriminatory. A volunteer secular chaplain at the Canberra hospital has lodged a complaint with the AHRC against the military chaplains program on the same basis.

On Thursday the AHRC welcomed the government’s commitment to introduce religious freedoms protection and called for the urgent repeal of laws that allow religious schools to discriminate against staff and students on the grounds of sexuality and gender identity.

Under another Ruddock review recommendation approved by the government, the AHRC will conduct an inquiry into the experience of discrimination and violence experienced by people of faith.