Dr Hollingworth, who devoted much of his life to fighting poverty, served as the Anglican archbishop of Brisbane for 11 years from 1990.
He died on Tuesday, aged 91.
Appointed governor-general in 2001 by former Liberal prime minister John Howard, Dr Hollingworth used his position to advocate for Indigenous rights and disadvantaged people.
But he spent less than two years in the role before being forced to resign.
In 2003, a board of inquiry into the handling of complaints of sexual abuse in the Anglican Diocese of Brisbane found that Dr Hollingworth, as archbishop, failed to act on knowledge of abuse.
He allowed two priests Donald Shearman and John Elliot to remain in the church despite knowing they had sexually assaulted children.
A church inquiry in 2023 found he had committed misconduct by allowing the pedophiles to remain in the church but said he remained fit for ministry.
Dr Hollingworth accepted the investigation's findings, saying he "made mistakes and I cannot undo them" but had committed no crimes.
In a statement on Tuesday, Anglican Archbishop of Brisbane Jeremy Greaves said the church sent its condolences to Dr Hollingworth's family.
"Anglican Church of Southern Queensland acknowledges with deep regret the past failings of the church," he said.
"(It) apologises unreservedly to those who have suffered abuse, distress, isolation, and harm caused by the church's failure to respond with integrity and care when it was needed most."
Dr Hollingworth was named Australian of the Year in 1991.
He announced in 2023 he would no longer practise as an Anglican priest to "end distress" for survivors.
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