GetUp! has claimed responsibility for a banner that unfurled during Senator Hanson's debut address on Wednesday, accusing the One Nation leader of accepting a $100,000 pay rise while opposing wage increases for workers.
The poster showed Senator Hanson surrounded by winged bundles of cash and wearing eight-bit sunglasses, which are a staple of online "thug life" memes.
"I quite liked the glasses GetUp! gave me in their new poster," she said in a post online, setting the image as her new profile picture on platforms including Facebook, Instagram and TikTok.
Government and opposition frontbenchers have expressed concern about the stunt, with coalition figures arguing it will likely improve Senator Hanson's political fortunes.
Nationals frontbencher Kevin Hogan said the move had "completely backfired" on the progressive campaign group.
"(It) makes them look like dills, and makes her look like a victim in the sense that she's being picked on, and that never works," he told ABC Radio.
The stunt was "counterproductive", Prime Minister Anthony Albanese told reporters on Thursday, while accusing some newspapers of giving One Nation free publicity.
"We need to turn the temperature down ... people should be allowed to address the Press Club with whatever views people have in a respectful manner," he said.
The National Press Club apologised to Senator Hanson and said two people entered the venue on Tuesday afternoon to install a drop-down screen without permission.
None of its staff or contractors had any involvement, the club said.
ACT Policing confirmed it received a complaint over the "alleged unauthorised access and interference with equipment" and said AFP was investigating.
In her lengthy speech on Wednesday, Senator Hanson said Australia needed to become a "monoculture", taking aim at radical Islam and transgender ideology, along with media outlets that she claimed treated her unfairly.
Her party clarified that migrants would still be free to speak their own languages at home if it were to win government, but they would need to be Australians first and put their ethnicity or creed second.
"They can be an Australian migrant, or an Australian-Italian, Australian-Greek, or an Australian-African. They're not African-Australians, they're Australians first," One Nation MP David Farley told ABC Radio on Thursday.
"There'll be times when they're bringing family and friends into the country on holidays etcetera, where that is adaptable ... but the reality is we've adapted English as a language, that's the Australian language," he said.
Australia's special envoy to combat Islamophobia Aftab Malik said Senator Hanson's comments, which included a fiery critique of "radical Islam", were opportunistic and fear-mongering.
"Australia is multi-religious, multi-ethnic, multi-faith. It's a rich dynamic culture in which people speak many different languages," he told ABC Radio.
"That's a dystopian vision that she has of Australia."
NSW Premier Chris Minns warned against importing US-style politics into Australia and said the drive towards personal attacks and endless fights was counterproductive.
Senator Hanson's rise in the polls was a reflection of working people feeling they were being economically left behind, YouGov director of public data Paul Smith said.
"Our polling shows that the number one reason for backing One Nation is not the leader, but the feeling of being unrepresented by the two major parties," he told AAP.
"For One Nation to win and keep the votes they have, they need to address the economic problems faced by working people about wages, housing, and generally being on their side of the economy."
A number of opinion polls have shown One Nation now leads political parties as Australians' first choice, while support for the coalition has plunged to record lows.
