The in-development project will tell the story of a lesbian couple and their diverse family, made up of a multi-ethnic mix of foster and biological children.
In a post on its website, One Million Moms has labelled the show "anti-family" and accuses ABC of having "lost their minds".
"ABC's Family Channel has several anti-family programmes, and they are planning on adding to that growing list," the post continues. "ABC Family has approved a series pilot from Jennifer Lopez's production company, Nuyorican, about a lesbian couple and their diverse family.
"Many families have already discovered that ABC Family Channel is anything but family-friendly. But because of family being part of the network's name, we thought a warning should still be sent out for anyone who continues to watch the channel."
One Million Moms further suggest that the concept of a lesbian couple raising children is not "acceptable content for a family show".
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"While foster care and adoption is a wonderful thing and the Bible does teach us to help orphans, this programme is attempting to redefine marriage and family by having two moms raise these children together," the post reads.
"Hollywood is continuing to push an agenda that homosexuality is acceptable when scripture states clearly it is a sin. As Christians, the Bible also says that we must speak up against sin. If we remain silent then we are guilty of sin also."
The post then encourages readers to "stop [the pilot] dead in its tracks" by contacting ABC Family, in order to "strongly encourage [the network] to drop all plans to air the programme".
One Million Moms previously targeted Ryan Murphy's comedy The New Normal - which follows a gay couple who have a child via a surrogate mother - and an issue of Marvel's X-Men comic which featured a gay wedding.
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