Opposition Leader Bill Shorten has suggested moves to oust ABC broadcaster Barrie Cassidy as chairman of an advisory board amount to a political witch-hunt.

Attorney-General George Brandis has thanked the Insiders host for standing down as chairman of the advisory board of the Australian Museum of Democracy at Old Parliament House.

Cassidy took on the unpaid position in August, but stepped down from the role on Friday morning after Mr Brandis asked him to do so.

Prime Minister Tony Abbott had raised concerns about Labor appointing "friends to all sorts of positions" in the dying days of the Rudd government.

Senator Brandis said the process for the appointment was "questionable".

But Mr Shorten says he does not think there was anything wrong with the way Cassidy's appointment was handled.

"We think that processes that are gone through should be respected. We don't believe in political witch-hunts," he said.

Sorry, this video has expired Barrie Cassidy speaks to News 24 before standing down from the advisory council

Senator Brandis said the museum must be seen to be apolitical, and it was not appropriate for a working political journalist to hold the chairman's role.

He said the circumstances did not reflect on Cassidy personally, and said the broadcaster's decision to stand aside was an "unselfish act".

In a letter to the director of the Museum of Australian Democracy at Old Parliament House, Daryl Karp, Cassidy wrote that he was resigning to prevent damage to the institution.

"I am of the belief that remaining in the position would shroud the board and the institution in ongoing controversy; and that's the last thing that I want," he wrote.

In his resignation letter, Mr Cassidy said Senator Brandis explained that he has "a strong view" that it is not appropriate for journalists or politicians involved in the political process to sit on such boards.

Analysis: Ministerial sound of silence The Abbott Government is entitled to wind back the media focus. But not to the point where routine scrutiny is almost impossible, writes Barrie Cassidy. Photo: AAP

On Friday morning, Cassidy defended his appointment and told News Breakfast he was approached in June to take over the vacant chairman position.

"It's an honorary position. It comes with no money. You volunteer your services," Cassidy said.

"It was signed off on in August and The Australian put it on page one and sort of said it was all shrouded in secrecy and so on."

Cassidy says he wants to know if other Labor government appointments will be reviewed to establish that there was nothing personal about Senator Brandis's request.

He says he is prepared to accept the Coalition has genuine concern about appointments in the last days of a government, but he wants evidence that it will be consistent.

He has requested that Senator Brandis outline what he knows about other appointments that were made around the same time.