Most people are unaware religious schools can sack teachers who are gay or who have children outside of marriage, a survey says.
The study also found an overwhelming majority - 89 per cent - back laws that would force such schools to publish their employment policies online and alert parents to them.
Canberra think tank the Australia Institute polled more than 1400 people nationwide about their views on education. Overall, parents nominated location as the main factor in deciding on which school to enrol their child, though values and academic performance were most important to those who opted for private schools.
Cost was the decisive factor for only 9 per cent of parents.
The institute also said 78 per cent of Australians were unaware religious schools were able to discriminate on the grounds of marital status or sexuality.
The exemptions, in federal and state legislation, allow religious organisations to sack employees, or reject potential recruits, if they do not conform with their beliefs.
Institute executive director Richard Denniss said that while few schools exercised this power, the public wanted those that did to be upfront about it.
''The Australian taxpayer invests a lot in the education of young people in both private and public schools.
''It's only fair that all schools that receive substantial funding from the public conform to the community's expectation of not only what is taught but how it's taught and by whom. Many private schools say they're not exclusive, yet there is nothing more exclusive than refusing to teach, or employ, a certain group of citizens.''
Independent Education Union federal secretary Chris Watt was uncertain how often the exemption was used when hiring staff.
However, he said most teachers employed in religious schools shared their employers' values.
''In the majority of workplaces, there's a large degree of tolerance. Some schools with a Christian faith place a lot of emphasis on their values, but teachers in those tend to embrace those values.''
Christian Schools Association chief executive Stephen Doherty said the schools he represented had nothing to hide.
However, advertising agencies sometimes refused to allow them to print, in job ads, that they preferred certain candidates.
''Our schools always advertise that they're seeking to employ people who are active participants in the Christian faith, except when some publishers refuse to allow them to use that wording … If a school wants to promote itself as holding a certain set of values, why wouldn't it disclose that?''
The federal government recently released a discussion paper canvassing changes to its anti-discrimination laws, though it has ruled out removing the religious exemptions.