If passed, any library that bans a book anyway would be at risk of losing its funding.
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It comes at a time when efforts to censor material have grown nationwide - much of it out of Florida.
The American Library Association says there were nearly 1,300 demands from various members of the public to censor library books and resources last year.
That's the highest number since the group started keeping such records more than 20 years ago.
"The amount of attempts to ban books or censor books in New Jersey and around the country has just skyrocketed," said State Sen. Andrew Zwicker.
The media outlet Tap into Roxbury recorded videos from a Board of Education meeting Tuesday night in Roxbury.
Some parents wanted nine books in Roxbury High School's library banned - mostly books like "Gender Queer: a Memoir" that discuss LGBTQ subjects.
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It's been a fight all school year with librarian Roxana Caivano. She decides which books are available, including books about both queer love and straight love.
She filed a defamation suit against four parents who she said called her a pornographer.
"If a public library is going to ban or censor a book, then the state has the authority to hold some or all of their public funding," Zwicker said.
The proposal also comes as poet and author Amanda Gorman announced on social media that her book, "The Hill we Climb," read during President Biden's inauguration, has been banned in a public elementary school in Miami-Dade County.
She said she was gutted by the decision.
The Roxbury BOE voted 6 to 4 to keep the nine books in question in the high school's library. One can be checked out only with a parent's permission.
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Zwicker said it's time for much more tolerance.
"Change is difficult and what we're seeing right now is people who are uncomfortable with some of this change being very, very loud," he said.
ALSO READ | Florida elementary school removes Amanda Gorman's poem from Biden's inauguration
Florida school removes from its library Amanda Gorman's poem from Biden's inauguration
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