Under the 1994 Local Government (Scotland) Act, councils have to appoint at least three members from churches who have voting rights.
One has to come from the Catholic Church, another from the Church of Scotland, and a third is appointed to reflect the religious beliefs of the area.
However, Edinburgh Secular Society (ESS) says the requirement no longer reflects the increasingly divergent views of society – including the rise of secularism.
The body also expressed concern that, in some cases, individuals who support more controversial views, such as Creationism, are being given a platform.
Professor Norman Bonney, a social science researcher and ESS founding member, said: "The legally required appointment of religious nominees to local authority education committees is profoundly undemocratic.
"This influence of unelected religious nominees on the decisions made by local council education committees can only further undermine public confidence in the accountability of local authorities to their local communities.
"There has to be a fundamental rethink of these arrangements."
Patrick Harvie, MSP for Glasgow, also opposed the appointment of religious committee members.
"In a society in which increasing numbers of people don't practice any religion, it's high time that we questioned a practice which gives religious hierarchies an influence over every child's education," he said.
"I'm particularly concerned at the involvement of people who would promote utterly unscientific notions like Creationism."
And Dr Nina Baker, a Glasgow City councillor for the Green Party, added: "While I can see that representatives of major world faiths might have a role in advising on curriculum content for the teaching of comparative religion in schools, I believe they should have no right to vote on councils' decision-making bodies."
However, the Rev Sally Foster-Fulton, convener of the Church of Scotland's church and society council, said she was "disappointed" by the suggestion religious representatives tried to undermine the democratic process.
"Instead of having a meaningful debate about the role of religion in a pluralistic society, we hear a misguided attack on people who give their time in the service of their community," she said.
"What the ESS consistently refuses to acknowledge is that most people in the Church are driven by a primary motivation of love, to serve others for the common good."
And Michael McGrath, director of the Scottish Catholic Education Service, said religious representatives reflected the long-standing involvement of Churches in Scottish education.
"Scotland's first schools were established in local parishes centuries before education authorities were established," he said.
Last year, there were calls for parents and pupils to be given greater influence over council decisions affecting schools.
The National Parent Forum of Scotland said more local authorities should allow representatives of pupils and parents to sit on council education committees.