Calls for a boycott ensued, with shoppers vowing to defect to rivals Aldi and Coles if Woolworths did not speak out against Corbett.
It comes as a business owner defends her decision to sack a contractor over posts made on Facebook in favour of a "No" vote.
"Woolworths is closer to home but I won't shop there again. Wanna know why? Ask Roger," one poster said.
"His comments were racist and hurtful and a lot of them were not even valid arguments," said another.
"You have lost a longtime customer thanks to Roger Corbett's comments on the 7.30 report tonight," a shopper wrote.
"I'm watching it now. I can't believe it. I will never shop there again," another replied.
The retailer's social media team was quick to jump in and remind protesters of its public stance in favour of marriage equality.
Roger Corbett, former managing director of Woolworths, is oppo...Roger Corbett, former managing director of Woolworths, is opposed to same-sex marriage.
He says same-sex relationships are similar to opposite-sex relationships but different. “A black man and a white man are equal, but they’re clearly different,” he says.
Posted by 7.30 on Monday, 18 September 2017
"We believe marriage equality is not just a social but also a workplace issue. For that reason, we pledged our support for marriage equality in August," Woolworths said in a stock response to each of the posts.
"We're proud to embrace diversity and want to be a community where all our people are free to be themselves without fear of prejudice or discrimination."
However, it added: "Diversity means recognising and respecting our differences, including religious and political beliefs."
A Woolworths supporter praised the retailer's response for "showing more balls than a Mardi Gras after-party!"
Many of those calling for a boycott mistakenly believed that Mr Corbett was the current managing director of the retail giant.
One commenter defended Woolworths, writing: "He was CEO 10 years ago! Your rants are doing the cause a massive disservice by evidencing how uninformed you on about the topic. Don't just get on the bandwagon because you think it's cool to speak up, do your homework!
"Ignorance and narrow-mindedness are the two biggest enemies of the SSM movement. Before you publicly deride Woolworths - make sure you're also not being narrow-minded or ignorant. "Listen to the facts and also accept that a 75-year-old conservative isn't going to change his opinion ... Emotional (and incorrect) outbursts are not the way to win this fight."
Another urged people to respect those whose views differed from their own, writing: "Everyone is entitled to their own opinion and beliefs. It seems like if someone is against this marriage equality thing then they get hated on and trolled. Yet people who are for it don't. Leave everyone alone. We all have our reasons to accept or go against this law."
Corbett was chief executive of Woolworths from 1999 to 2006 and is now a director of Wal-Mart, the Reserve Bank of Australia and Fairfax Media.
Last year, he refused to confirm or deny rumours of a rift with Woolworths' current boss Brad Banducci.
Corbett was appointed as an adviser to the board in late 2015, before Banducci took the reins at the company.
He resigned from his consultancy post in July 2016, saying at the time that it clashed with his other commitments.
