The demand was set out by the Family Education Trust to politicians scrutinising the impact of the Scottish Government's Marriage and Civil Partnership Bill.
Trust spokesman Michael Calwell said: "We need first of all what you might call a statutory obligation to inform parents if any teaching about marriage, which conflicts with their view, is raised in the classroom.
"The second thing would be the right to withdraw from that, and the third thing would be a positive obligation of the state to actually provide them with education that does conform with their understanding of the vital, pre-political if you like, nature and purpose of marriage."
Mr Calwell's views were heard by MSPs on Holyrood's Equal Opportunities Committee, which was also attended by representatives from teachers' union the Educational Institute of Scotland, gay rights group Stonewall, the police, NHS and the Scottish Catholic Education Service.
He also argued that growing numbers of immigrants with strong views on traditional marriage could pose problems for society, should the legislation become law.
"You have to be mindful of the way Scotland is changing, particularly with the inflow of people from very strong pro-family, pro-marriage cultures," he said.
"This is visibly the case, particularly where I live."