California is poised to become the first state in America to make the teaching of positive contributions made by gay and lesbian people to US history and society compulsory in public schools.

The governor of California, Jerry Brown, must decide whether to incur the wrath of religious and conservative groups lined up against the move and approve a bill that has now cleared both houses of the state assembly. If signed into law, it would require the rewriting of school textbooks and redrawing of the social science curriculum to include lesbian, bisexual, gay and transgender history – a move that could have wide ramifications given that California's school roll of 6.2 million children is the largest in the country.

Supporters argued that it would give gay teenagers role models and help combat homophobic bullying. It would redress the imbalance in state schools that are already required to teach about women, entrepreneurs and labour and minority ethnic groups including African-Mexican- and Native Americans.

"We gain a greater appreciation for what it means to be an American," John Pérez, the first openly gay speaker of the Californian assembly, told the San Francisco Chronicle.

During debate about the bill, supporters gave examples of historical figures they said would be featured, including Friedrich von Steuben, a military adviser to George Washington forced out of Prussia because he was gay, and the British mathematics genius Alan Turing.

Opponents, including all but one of the assembly's Republicans, criticised the bill as unnecessary and objectionable. "Our founding fathers are turning over in their graves," Republican Tim Donnelly told Associated Press.

Some opponents, such as the campaigning website SaveCalifornia.com, are encouraging parents to take their children out of state schools.

A similar bill was vetoed by the previous California governor, Arnold Schwarzenegger. Brown, who took over the post earlier this year, has given no indication whether he will sign or veto the legislation. Once he receives the bill, probably this week, he will have 12 days to make his decision.

• This article was amended on 7 July 2011. The original sub-heading referred to governor Gerry Brown. This misspelling has been corrected.