But Senator Fierravanti-Wells warned a minimalist bill that "merely substitutes religious discrimination for sex discrimination or racial discrimination" will not make voters' concerns go away. The NSW Liberal said Prime Minister Scott Morrison had "created a greater expectation that he will do something substantial" on religious freedom, pointing to his public appearance worshipping at a church service during the election campaign.

Noting swings against Labor in seats with high levels of religious voters in western Sydney, Senator Fierravanti-Wells said concerns about religious freedom "moved votes" at the May election. The former minister for international development - who quit the frontbench in protest against Malcolm Turnbull's leadership last year - said both sides of politics ignored peoples' concerns about religious rights at their peril.

"It might turn out to be a pox on both their houses," she said.

Last week, Senator Fierravanti-Wells launched an official parliamentary petition calling on the public to pressure the upper house to ensure "freedom to manifest one's religion" would only be limited by the the need to protect public safety, health or the rights and freedoms of others. She said the Folau matter had "hardened my resolve on this issue".

The government announced it would introduce a religious discrimination bill late last year, in response to the Ruddock review into religious freedom. Mr Porter held a meeting of about 22 MPs government MP in Canberra on Friday, where he showed them a PowerPoint presentation on the bill. Other MP briefings are expected to take place in the coming weeks.