"The elevation of this issue again in the Labor leadership contest is unhelpful if the party wishes to appeal to a broad cross-section of the Australian community," according to ACL managing director Lyle Shelton.
Mr Shelton said many Christians resonated with the policies of the Labor Party but calls to have a binding vote on same-sex marriage would be a turnoff for many Christians and Labor voters.
"Labor's 2014 National Conference should really be focussing on how the party can better appeal to the centre on social policy, including how best to promote policy which supports, wherever possible, a mother and father for children," he said.
"This issue has had a fair go over the past three years. It would be damaging for to Labor continue to tie itself to this agenda."
Mr Shelton said 84 laws were changed in 2008 that removed discrimination from same-sex couples.
"After two parliamentary inquiries found no discrimination in Australian law against same-sex couples and several votes rejecting changing the definition of marriage, it is time to move on," he said.
"We've just had an election fought in part on this issue and the result was the worst Labor vote in 100 years.
"The party of same-sex marriage, the Greens, lost 600,000 votes in a 3 per cent swing against them," he said.
Mr Shelton said polling commissioned by ACL and conducted by JWS Research immediately after the September 7 election showed same-sex marriage is a low order issue with voters.
"Just 15 per cent of Labor voters said it was a top three issue influencing their vote while just four per cent of Coalition voters rated it as important," he said.
"Seventy-two per cent of Greens voters are not energised by the issue.
"It is important that Labor maintains its ability to appeal to a broad range of people in the community," he said.
