Several Australian bars have dumped Coopers Brewery after it was featured by religious group the Bible Society.
The video shows two MPs debating their opposing views on same-sex marriage - which is not legal in Australia - as they clutch Coopers beers.
It has led to claims Coopers is against marriage equality, a claim it denies.
The backlash has gathered pace in recent days and, by Tuesday, a string of drinking spots in favour of same-sex marriage had boycotted the brand.
The Bible Society posted the "Keeping It Light" video on Thursday. It features conservative MPs Tim Wilson (for same-sex marriage) and Andrew Hastie (against) debating the issue in what they call a "civil and respectful way".
Coopers has since claimed it "did not give permission" to be included in the video. However, the brand recently celebrated the Bible Society's 200-year anniversary with a commemorative beer featuring Bible verses.
In the video, Mr Wilson argues: "I believe that it would be sensible to change the act that deals with issues around civil marriage to include two people regardless of their gender."
Mr Hastie counters: "I'm for retaining the current definition of marriage, which is between a man and a woman."
Despite Mr Wilson's inclusion, critics interpreted the video as one-sided. One commentator said Coopers risked sponsoring a "political act by a religious organisation", while another said "homophobia lite is still homophobia".
"I have respected Coopers all my life, and it was crushing to realise that as a queer person, they don't respect me," wrote Chloe Sargeant for the Special Broadcasting Service.
Opposition to the video has picked up steam since the weekend. By Tuesday, at least eight drinking spots in Sydney and Melbourne had publicly declared they would not stock Coopers. One widely shared video showed two people throwing full bottles in the bin.
Luke Hiscox, from Sydney's Union Hotel, which plans to take Coopers off tap, said people were upset by the phrase "keeping it light".
"That irks people because for them it's not in the slightest a light topic," he told the BBC.
"I don't think they really realised what they were saying."
Another venue, The Old Bar in Melbourne, said it would boycott Coopers because it was "very obvious that our values are at odds".
In a statement, Cooper said it was not "trying to push a religious message" with its commemorative beer range. It maintained it had not sponsored the video.
"We respect the beliefs of our community and do not wish to try and change them," the company said.
In a subsequent statement, it said it had cancelled the release of its Bible Society commemorative cans and would be joining Australian Marriage Equality. ""Our company supports marriage equality," Director of Corporate Affairs Melanie Cooper said.
Bible Society chief executive Greg Clarke said the video sought to have a "civil conversation on a serious issue".
"At first I was surprised the reaction was so immediate and extreme, but then on reflection [I] wasn't surprised because this really seems to be how social media works at the moment,"  he told the BBC.
Mr Wilson has described the boycott as absurd, saying it only proves the value of the discussion.
"I'm disappointed Coopers appears to have distanced themselves from a sensible conversation that they should be proud to align themselves with," he told news.com.au.
Advertising commentator Jane Caro agreed the video was not promoting a view. She said same-sex marriage advocates were often suspicious of religious messaging.
"They have lost patience and lost tolerance for the idea that there should be mutual respect on both sides," Ms Caro told the BBC.
"I think Coopers have probably inadvertently found themselves in the eye of the storm."
Australia's largest independent beer company has found itself at the centre of a boycott over a video discussing same-sex marriage.