Pushing for same-sex marriage in the short term without further religious protections would “put plural and tolerant democracy at risk”, the chair of a Senate inquiry into marriage equality has said.

Liberal senator David Fawcett told Guardian Australia much broader protections for religious groups were needed before a bill could progress.

He said that should include consideration to allow florists, bakers and photographers to reject same-sex weddings on the basis of their religious beliefs, throwing up a further potential roadblock to a free vote.

Labor and Australians for Equality both rejected that call to wind back discrimination law, arguing it had nothing to do with the marriage law.

On Wednesday the committee examining the government’s exposure draft bill released a report calling for several proposed forms of discrimination against LGBTI people to be removed.

The consensus report raised hopes of advocates, Liberal moderates, Labor and the Greens who hope to achieve marriage equality this parliamentary term with a cross-party or government bill.

Responding to the report, Malcolm Turnbull and finance minister, Mathias Cormann, reiterated that the plebiscite on same-sex marriage is government policy, although Turnbull’s remarks left open the possibility the party room may change tack.

The consensus report the committee said that “broader reform should be reconsidered to advance protections for religious freedom”, specifically adding religious belief as a protected attribute in discrimination law.

While tabling the report in the Senate on Wednesday, Fawcett said that process would have to occur alongside legalisation on same-sex marriage, not after.

On Thursday, Fawcett said in a statement that while the committee agreed on solutions in a few areas, “the majority of the report identifies areas where ... the issues dividing opinion were complex, requiring careful consideration if religious freedoms were to be protected and rights balanced”.

“Proponents of changing the definition of marriage who say ‘let’s have that vote, it’s pretty simple’ or that it is ‘a simple, overdue change that sends a powerful message’ are putting our plural and tolerant democracy at risk,” he said.

Fawcett cited the decision by then attorney-general, Mark Dreyfus, to delay discrimination law reform in 2013 because freedom of speech and religion needed careful consideration as they are fundamental to democracy.

Dreyfus, now shadow attorney general, told Guardian Australia the quote had “nothing to do with the legislation for marriage equality, and the use of my words out of context is wildly inappropriate”.

Australians for Equality co-chair, Anna Brown, said making religion a protected attribute would prevent religious people from being discriminated against in education, employment or seeking goods and services, and was “not about giving a service provider a right to discriminate” against same-sex weddings.

In 2013 the Abbott-led opposition had agreed individuals should not be able refuse to sell goods and services based on their private religious belief, Brown said, and the Turnbull government exposure draft had passed cabinet without the further exemptions to discrimination law Fawcett was now calling to be considered.

“If members think same-sex marriage shouldn’t proceed without these changes, they can exercise their individual vote to reflect that – but there’s no way this should be holding up marriage equality itself.”

On Wednesday evening Turnbull said the government “took a plebiscite to the last election and we haven’t determined what our policies will be at the next election”.

Asked if the plebiscite would remain Coalition policy, he said it would be decided “closer to the next election”.

“But our policy at the moment, right now, is that we will not support the introduction of a bill on same-sex marriage until there has been a plebiscite, a vote of all the Australian people endorsing it.”

The statement maintains Turnbull’s position after Labor decided to block the plebiscite, refusing to rule reconsideration of a free vote in or out.

On Thursday, Cormann said the plebiscite remains Coalition policy.

“The work the Senate select committee did is in the scenario where a future plebiscite were to make certain decisions which would lead to certain outcomes,” he said.

“We have not had a plebiscite. So from that point of view our policy remains to have a plebiscite first.

“The best way to settle a diversity of strongly held views is by giving the Australian people their say.”