What transpired in the years before the moral majority came to prominence that would have created the need for such an organization in people's minds?

Well as they exist to propagate a political agenda that is not in step with 80% of the american people then there was no need for such a falsely named organization to exist. See, the only reason that they exist is to impose a morality that they don't really care about onto the rest of the people. Hope this is clear for you

During the paleolithic, hominins grouped together in small societies such as bands, and subsisted by gathering  plants  and fishing, hunting or scavenging wild  animals. the paleolithic is characterized by the use of knapped stone tools, although at the time humans also used  wood  and bone tools.

Some states did honor the voting rights for women