Australia's business leaders and biggest corporations are being bullied by activist groups into supporting same-sex marriage laws, Immigration Minister Peter Dutton said on Friday.

Days after brewing company Coopers moved to head off a boycott of its products after Liberal MPs Tim Wilson and Andrew Hastie appeared in a video debating same-sex marriage reforms, Mr Dutton told Sydney radio host Ray Hadley that big corporations including Qantas were afraid of being targeted online by activist groups.

"We need to have the ability for both sides to be heard and we're in a politically correct age it seems, which I can't tolerate, and I think a lot of Australians are of the same view," he said.

Mr Dutton said he wanted a respectful debate on marriage equality, but added that publicly listed companies shouldn't take political stances and business leaders should not prioritise debating moral issues over running their companies.