Banning books on same-sex parenting from local libraries has also placed Cumberland City Council's funding under threat as the NSW government investigates.
The council, which covers a population of about 240,000 people living near Parramatta, narrowly voted in May to "take immediate action to rid same-sex parents books/materials in council's library service".
The motion passed by six votes to five.
The state body in charge of administering anti-discrimination laws is "deeply concerned" over the ban.
"We live in a diverse and multicultural society, and it is important that our diversity is represented in the books available to our communities," Anti-Discrimination NSW president Helen McKenzie said.
"For rainbow families living in the Cumberland council area, this is a hurtful and divisive act which impacts them and their children.
"It also impacts non-rainbow families who wish to teach their children about acceptance, diversity and inclusion."
NSW Arts Minister John Graham says councils should not get involved in censorship. (Dan Himbrechts/AAP PHOTOS)
Ms McKenzie declined to comment on whether any complaints had been made to her agency due to legislated secrecy provisions.
But NSW Arts Minister John Graham said banning books was a bad sign for civilisations, adding local councillors should not engage in censorship.
"It is up to readers to choose which book to take off the shelf," he said.
"We are examining the consequences this decision may have for the council continuing to receive library funding from the NSW government."
Mayor Lisa Lake was among the councillors who voted no, adding she vehemently disagreed with the decision.
Five copies of the book A Focus On: Same Sex Parents have been in the council's libraries since 2019.
It forms part of a series that aims to inform children about "difficult realities" and "healthy ways for children to process and understand them".
"Rather than have people complain to me about the book, I'm now getting a lot of people who are disappointed with the decision and wishing us to reverse it," Ms Lake told ABC Radio.
The councillor who put forward the motion, former mayor Steve Christou, said the community wanted the book banned.
"I'm only representing the values of our community and what the majority of people are telling us ... we're not marginalising anyone here," he said.
The majority of voters in Cumberland's four electorates opposed legalising same-sex marriage during 2017's national postal survey.
Federal Arts Minister Tony Burke said libraries were for learning and to help people understand each other.
"Banning books takes things in the opposite direction and serves no one," he said.
Sydney independent MP Alex Greenwich, who is gay, criticised the ban on social media.
Cumberland local Caroline Staples said the area welcomed people of all backgrounds and beliefs and the move crossed a dangerous line.Â
Her petition to overturn the decision has received backing from Equality Australia ahead of a council meeting on May 15.
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