Supporters of the referendum say the new law would expose young children to sex and infringe on parental rights.
The group has until Oct. 12 to collect 504,760 signatures from registered voters to qualify the measure for the ballot.
The new law, Senate Bill 48, was signed by Gov. Jerry Brown in July.
It will take effect Jan.1, but state education officials say it is unlikely to be fully implemented until at least the 2015-16 school year.
It adds lesbian, gay, bisexual, transgender people, as well as European Americans and people with disabilities to the lengthy list of social and ethnic groups whose "roles and contributions" California public schools must include in state and U.S. history lessons and teaching materials.
The Associated Press contributed to this report.