Telstra is facing a public backlash after toning down its support for same-sex marriage.

The telco giant signed up along with more than 800 other companies in 2015 to back a campaign for marriage equality in Australia.

But on Wednesday reports emerged that Telstra had backed away amid pressure from the Catholic church.

Telstra insists it supports diversity and inclusion but has no plans to be an active participant in the marriage equality debate.

The news sparked a massive backlash on social media, with Telstra accused of being 'weak' and 'gutless'.

'What's your stance on blackmail from religious organisations?' Western Sydney councillor Natasha Coster tweeted.

One man, Dan, condemned Telstra for removing its support, saying involvement in public debate was what drove change.

'Public debate is what drives change. Removing your public support to safeguard your profits says you are cowards,' he tweeted.

Some customers said they would be tearing up their Telstra contracts.

'I'll be leaving Telstra today. Its service is as unreliable and inconsistent as its support of equal rights for its customers,' Tony Broderick tweeted.

Telstra's decision came after the archdiocese of Sydney business manager Michael Digges wrote a letter to companies after they publicly backed a full-page advertisement released by Marriage Equality Australia calling for same-sex marriage laws in May 2015.

Telstra decided to back away from the campaign as it did not want to risk its deal with the church to provide services to Catholic schools across the country, The Australian reported.

A Telstra spokesman said as the federal government had decided to call a plebiscite on the issue, it was up to parliament to decide whether same-sex marriage laws should be introduced.

'Our people and stakeholders can contribute to this process and out of respect, it is important we allow them to voice their own views,' he said.

'Given this we have no further plans to be active in the debate.'

More than 860 companies including the big four banks, Qantas and Coca-Cola Amatil joined Telstra in backing Australian Marriage Equality's campaign.

Telstra's logo still appears alongside those of other companies on Australian Marriage Equality's website.

AAP understands that the Catholic church, along with other religious groups, wrote to the companies that signed up to support the campaign expressing concern about their involvement.

Australian Marriage Equality director Rodney Croome said Telstra had not told the organisation of any change in position on same-sex marriage.

The number of companies that backed the campaign for same-sex marriage had doubled in less than a year, he said.

'The Catholic church has every right to express its views but corporate Australia isn't listening,' Mr Croome told AAP.

The Archdiocese of Sydney confirmed Mr Digges wrote in June to several companies that backed the Australian Marriage Equality campaign, and had business dealings with the Catholic Church.

But Mr Digges had never threatened to boycott companies that supported the campaign, the statement said.

'Mr Digges pointed out that support of same-sex marriage is incompatible with the business practices of the Catholic Archdiocese of Sydney,' it said.

'In turn he also said in agreeing to do business with the archdiocese, our business partners and suppliers agree to be comfortable with the association of their name and brand with the archdiocese.'

Mr Digges said he had serious concerns about businesses promoting and identifying themselves with social-issue campaigns on behalf of staff, shareholders, customers, suppliers and other stakeholders.

AAP