Cumberland City Council faced pressure from the public as well as state and federal politicians after passing the ban on May 1.
Local grandmother Caroline Staples said more than 50,000 people had signed a petition calling on the council to lift the ban.
Staples said her bid to overturn the ban was supported by leading bodies such as the Australian Library and Information Association, Early Childhood Australia and Equality Australia.
“The book banners showed that they don’t care about the well-being and safety of our children and families,” she said.
“I am optimistic that councilors have now had a chance to consider the consequences of their decision to reject this divisive move.”
At least 40,000 people have signed a petition from the Equality Australia Petition, including 2,194 of Cumberland’s postcodes. A further 10,065 have signed a change.org petition and the petitions will be presented together to the council.
The book titled Same-sex parents by Holly Duhigg, is one of the books the council removed from its libraries.
Equality Australia legal director Ghassan Kassisieh said the book was part of a series on different types of families.
“Trying to erase these loving families from library shelves is importing the worst of the American-style culture wars and does not reflect what modern Australia looks like or wants,” he said.
“People should be able to go to their public library and find books that represent their families. If someone doesn’t like what’s in a book, they don’t have to borrow it.”
“We have constant complaints from local residents about these kinds of books and similar issues infiltrating our libraries,” he said.
Council will vote on a motion to change or remove the Cumberland Library Strategy Amendment at the next council meeting tonight.