Mr Brandis said parliament would start the debate on same-sex marriage legalisation with Senator Smith's bill, if a "yes" vote is victorious.
"The people are being asked if we should treat LGBTI people equally".
'While the Law Council does not endorse every detail of the Smith Bill it represents a better balance from a human rights perspective and represents greater fairness, including those affected by winding back anti-discrimination laws, ' Ms McLeod said.
"That would be profoundly disrespectful and a rebuke to the people of Australia".
While businesses would be able to boycott gay marriages, they would otherwise have to comply with existing anti-discrimination laws.
'The right to freedom of religion also appears in worldwide law. We know that's the real slippery slope, when you unravel anti-discrimination protections, and I don't think Australian people want that.
"There is no apology for the fact that the Bill does not address free speech or parental rights - because it's a Bill about marriage equality".
The group said in a statement: "We feel that it is important to offer our community the support that will be needed at this historical moment, and hopefully the opportunity to celebrate as well".
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Senator Paterson told the ABC in his view it would be wrong for a shop to erect a sign saying "no gays", but it would be okay if the sign said "no gay weddings".
This legislation echoes fears voiced by the "no" campaign in Australia, which promoted myths that same-sex marriage would lead to "compulsory" gay sex education courses as well as cross-dressing kids.
Opposition Leader Bill Shorten said Labor would give the Smith bill "very favourable consideration".
"You could potentially see a situation where a hire auto company could leave their customers stranded on the way to a marriage ceremony simply because the driver held a thought or belief against it. As a non-religious person, I should have no fewer rights to live my life consistent with my beliefs than anyone else".
The proposed bill has been heavily criticised by supporters of gay marriage with Alex Greenwich, co-chair of Australian Marriage Equality, claiming it has the potential to "divide Australians".
Sen. Dean Smith, a member of the ruling Liberal Party (which is actually conservative), drafted a bill with bipartisan support that would give religious officials the power to refuse to marry same-sex couples.
LGBT activists also said this bill runs counter to the will of the Australian people casting a vote for equality, not a "license to discriminate".