Members of the SSS were giving evidence to Holyrood's Public Petitions Committee on their petition, which calls on Education Secretary Mike Russell to issue guidance to publicly-funded schools and colleges to ''prevent the teaching of creationism and related doctrines as viable alternatives to established science''.
Creationism is the belief that the universe and living beings originate from acts of divine creation.
SSS chair Spencer Fildes highlighted the outcry over the involvement of the US-based religious group Church of Christ at Kirktonholme Primary School in East Kilbride, South Lanarkshire, last year, saying the material distributed to pupils there "beggars belief".
He told MSPs: "Other creationist organisations also distribute materials or actually offer speakers to schools.
"Numerous schools are known to have creationist chaplains and creationist denominations, including US-inspired extreme creationist sects."
Mr Fildes said his organisation had evidence of examples at schools in Clackmannanshire and Falkirk as well as South Lanarkshire.
He said: "It is no longer credible to ignore the fact that there are organisations attempting, and with some success, to penetrate our schools in order to present creationism - young earth doctrines - as a valid alternative to established science.
"It is rarely the teachers themselves that are actually the problem, but volunteer visitors and externally-funded chaplains, whose offerings are often gratefully accepted by the schools, who are currently coping with many other pressures.
"It is no longer credible to deny that this is a problem in need of official attention."
Asked about what potential teaching creationism has to harm pupils, Mr Fildes said: "The worst that can happen is a distortion of learning in the classroom.
"From a young age, I would be horrified to think that there was any potential for those minds to be distorted in any way.
"Why should we assert such untruths to our children in an educational establishment, particularly the science class?"
Professor Paul Braterman, SSS board member and scientific advisor, said: "If you tell children untruths at a stage when they are going to believe you, that is going to affect their outlook on life indefinitely."
The committee heard the petition has nearly 700 signatories including teachers, ministers of religion and three Nobel prize scientists.
Mr Fildes said: "We're not asking for a massive change to the legislation, we're not asking for much here.
"We're just asking for guidance to be issued to rid any ambiguity around this."
Calling for the petition to be closed, SNP MSP Chic Brodie said: "We've already had as recently as August a statement from the Government in terms of the tradition that we should not determine the curriculum and it's a matter for the educationalists."
Independent MSP John Wilson said: "I think there needs to be a clear steer given to teaching staff about what is permissible to be taught within the lessons."
The committee agreed by majority to write to the Scottish Government and educational institutions for their views on the matter.