NSW, Western Australia and South Australia are supporting the Commonwealth's arguments defending the 2013 dismissal.

Michaela Banerji's lawyers last week told the court her anti-government tweets were anonymous, and argued the then-Immigration Department risked shaking public faith in its own work by outing her as their author.

Lawyers representing NSW, Western Australia and South Australia's governments made written submissions to the court last month denying Ms Banerji's use of the pseudonym @LaLegale should have exempted her from punishment.

The states' entry into the court case signals its potential to undermine their own constraints on public comment from bureaucrats.

Ms Banerji's employer sacked her under laws requiring bureaucrats to uphold values of impartiality in the Australian Public Service, Western Australia's solicitor-general Joshua Thomson and assistant state counsel Nick John said.

"The reputation of the APS may well be affected if an APS employee acts anonymously, but the action is later linked back to the employee or the APS more generally. That has occurred here," they said.

South Australian solicitor-general Chris Bleby and legal counsel Lauren Gavranich rejected an appeals tribunal finding that favoured Ms Banerji by saying anonymous comments could not be used to draw conclusions about the professionalism or impartiality of the public service.

"Integrity in the structure of responsible government has an absolute quality: it requires that there will be some circumstances in which some employees, especially senior ones, may be judged accountable for their behaviour, whether they intended anonymity or not."

Arguing for NSW, solicitor-general Michael Sexton and lawyer Frances Gordon said a "bright line of distinction" between open and anonymous comments couldn't be drawn, given Ms Banerji was outed as the author.

In submissions following those from the state governments, her lawyers last week said the Immigration Department - now called Home Affairs - discovered she wrote the tweets by examining a folder on her desk in 2012. It later revealed her identity.

Conservative government-led NSW and South Australia, and Labor-run Western Australia, told the court Ms Banerji's sacking and its restriction on her free speech justifiably protected public confidence in an apolitical and impartial bureaucracy.

"It is not appropriate for the public servants who are responsible for implementing these policy decisions to be seen to have separate views that may conflict with the policy decisions of the elected representatives," Mr Thomson and Mr John, writing for the WA government, said.

"The public would then correctly apprehend that the unelected representatives may endeavour to subvert the policy decisions made by the people who had been elected by the public.

"As well, elected ministers may well lose confidence in the public service to faithfully implement policy decisions. In both cases, representative democracy is undermined."

Limits on government power to punish public servants for misconduct made the laws - and her dismissal - consistent with the right to free speech implied in Australia's constitution, Mr Sexton and Ms Gordon said.

"That judgment, and the sanction imposed, were each able to be reviewed on their merits, to protect against the possibility of capricious or disproportionate exercises of power."

Attorney-General Christian Porter intervened after Ms Banerji won an appeals tribunal case against the federal workplace insurer's refusal to compensate her for the psychological condition that developed after she was sacked over her tweets.

The tribunal in April found the government "impermissibly" trespassed upon Ms Banerji's freedom of political communication and was wrong to sack her.

Mr Porter removed the government's Federal Court appeal against the finding and sent it to the High Court, flagging the case's potential to undermine the government's policy stopping public servants from expressing their political views on social media.

The federal government is expected to reply to arguments from Ms Banerji's lawyers on December 19.