At least one same-sex marriage opponent believes it will be highly unlikely additional religious protections will get the support of federal parliament.
Cabinet minister Peter Dutton wants further safeguards added to a private bill that allows same-sex couples to marry, but admits that will be "near impossible" given the numbers in the lower house.
"In this business, we face the reality of arithmetic and that is the reality in this parliament," he told colleagues on Monday night.
Mr Dutton is against changing the Marriage Act, but has committed to voting 'yes' out of respect of the result of the postal survey - an idea he put forward when Tony Abbott's compulsory plebiscite failed.
He will, however, support "sensible" amendments to be put forward by his Liberal colleagues, including conservatives Michael Sukkar and Andrew Hastie.
They are seeking wide-ranging changes, including exemptions for civil celebrants, small businesses and religious charities, and two definitions of marriage - one for men and women, and another for two people.
Members of Australian Christians for Marriage Equality were in Canberra on Tuesday to lobby MPs against the amendments.
Uniting Church minister Margaret Mayman said there was a chorus of conservative Christian voices seeking to undermine the will of the Australian people.
"We believe there's no basis, in either democratic principles or Christian faith, for introducing amendments that are arbitrary, divisive and unnecessary," she told reporters.
Anglican priest Angus McLeay dismissed as a "myth" claims the charity status of religious bodies was being threatened.
"Plenty of Christians are completely relaxed about this law going through. It's not an issue for their faith - millions of Christians voted 'yes'," he said.
Mr Dutton denied the amendments were an attempt to frustrate the process and delay the bill's passage, and would instead improve the legislation.
"I do believe Australians would support those safeguards, that's why it is important for us to have another process ... because I think there is a debate to be had in this country around religious and parental protections," he said.
The immigration minister believes enshrining further protections will have greater success following an inquiry into religious freedoms early next year, to be led by Philip Ruddock.
