Would this fictional religion do well in my Anti-Christian Patriarchy story?

You could say its a sect of Christianity , called Adamism, but it wouldn't be a religion. It would be a denomination. A lot of Fundamentalist Christians would follow suit to these beliefs. And if you were talking about writing abook with this in it, and trying to portray it as the ' good ' way, then try not to allow the word , radical, in the description. Such if it was their own people talking about this, followers of Adamism wouldn't call it Radical they would call it right. However if you are trying to portray the belief in the story as crude and corrupt, then it would be ok to claim it as Radical.