Comments from Safe Schools Coalition manager Roz Ward labelling the Australian flag as racist highlight the concerns people have with the program, Prime Minister Malcolm Turnbull says.
A rainbow flag was hoisted above Victorian parliament on Tuesday after Premier Daniel Andrews apologised to the LGBTI community for past laws that criminalise homosexual behaviour.
According to News Limited reports, Ms Ward posted a picture of the rainbow flag to her Facebook account with the words: "Now we just need to get rid of the racist Australian flag on top of state parliament and get a red one up there and my work is done".
Ms Ward announced her resignation from an advisory role with the Victorian government on Friday night and expressed regret for her comments.
"I apologise for any offence that comments, posted on my private Facebook page, may have caused the government and members of the LGBTI community," she said in a statement.
"These were private comments that were never intended for the public domain."
Prime Minister Malcolm Turnbull said Ms Ward's actions underlined concerns many people had about how the program was managed, but said his government was committed to zero tolerance on bullying.
"Kids should be safe from bullying, whether it is on the basis of their sexual orientation, their race, their religion, their appearance, right across the board," he told reporters in Sydney.
Federal Opposition Leader Bill Shorten said he didn't agree with Ms Ward's flag comments, but they had nothing to do with the Safe Schools program.
"I don't buy that sort of tenuous lunar right logic (that) because one person has criticised the flag, we shouldn't have anti-bullying programs in our schools," he told reporters in Melbourne.
The Safe Schools program was set up to stop the bullying of gay and transgender students.
In March, the federal government announced sweeping changes to the program after an independent review found a number of lessons and content were inappropriate for children.
Conservative politicians led a backbench revolt against the program before the government decided to review it.
The Safe Schools Coalition is made up of organisations and schools working together to create safe and inclusive school environments for same sex attracted, intersex and gender diverse students, staff and families.
A Victorian government spokeswoman said it was Ms Ward's decision to resign.
Opposition spokesman Nick Wakeling described Ms Ward's post as "appalling".
