Churches hold the balance of power in nearly two- thirds of council education committees due to a law compelling councils to appoint three religious representatives, the secular coalition said.
The Edinburgh Secular Society (ESS) has lodged a petition to repeal the law, backed by The National Secular Society, Humanist Society Scotland and the University of Edinburgh Humanist Society, with the support of Green MSP Patrick Harvie and SNP councillor Sandy Howat.
Mr Harvie is particularly concerned about the promotion of creationism in schools, while Mr Howat said the churches' right to unelected representation on boards was undemocratic and untenable.
The petition calls for a repeal of section 124 of the Local Government Act, ensuring religious representation on boards, following recent census results showing nearly half of Scots profess no religious beliefs.
Colin Emerson, ESS vice-chair, said: "To afford a particular section of society a privileged position within the decision making process of local government, based solely on their particular and personal religious beliefs, is profoundly and inherently undemocratic, unfair and discriminatory."
Mr Harvie, MSP for Glasgow, said: "I'm particularly concerned at the involvement of people who would promote utterly unscientific notions like creationism. Pushing this absurd ideology at children is the very opposite of education."