The Humanist Society Scotland is asking parents to support a new petition calling on the Scottish Parliament to give headteachers the right to adopt a "non-religious community schools model" as an alternative to the current non-denominational and denominational system.
Polling by Survation found that 60 per cent of people would support such non-religious schools, open to children of all faiths and none, while 22 per cent neither support or oppose the idea.
A further 10 per cent of those surveyed were opposed while 8 per cent did not know.
At present, Scottish pupils can attend a state-funded, non-denominational school and be "opted-out" of religious observance but the Humanist Society argues this could lead to children being stigmatised among their peers.
The survey, in which 1,002 Scots were questioned, also found that only 40% agreed with this.
A further 39 per cent did not believe opting out of activities such as religious services would results in stigmatising while the remainder did not know.
Commenting on the findings, the charity's chief executive Gordon MacRae said: "Today's figures demonstrate the broad support for a new, inclusive form of non-religious community school that reflects the diversity of modern Scotland.
"Many parents assume that only denominational schools in Scotland are faith schools.
"They are shocked when they learn that their local non-denominational school still host end-of-term prizegivings and whole school gatherings in a church as part of a churchservice.
"Today's figures reflects the fear of many parents that opting their child out of religious observance will stigmatise their child.
"Whilst there has been progress in schools that now include speakers from other faith and belief bodies, the law remains clear - non-denominational schools must provide religious observance that reflects the Christian heritage of Scotland."
He added: "We hope that the Scottish Parliament will listen to parents and expand the options available to educators, parents and pupils, and establish non-religious community schools for the first time in Scotland."
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