Members of The Equality Network said they are worried that a section of the proposed law that would legalize gay marriage resembles a Section 28 clause that was repealed in 2000.
Section 28 forbade the promotion of homosexuality in schools or teaching that it was an acceptable family relationship, The Scotsman, of Edinburgh said.
A consultation of the bill and its implications in education is under way, The Scotsman said.
In its consultation response this month, Scotland for Marriage, a group backed by the Catholic Church, said it is "concerned that children will be taught in school sexual health education that marriage can be between two people of the same sex."
A Scottish government spokesman did not comment directly on the matter.
"The Scottish government is introducing same-sex marriage in Scotland because it is the right thing to do, and is striving to create a Scotland that is free, tolerant and fair."