Is religious innovation an oxymoron?
Innovation is usually associated with scientific breakthrough. But to some people, breakthroughs come in the form of religious disputes between their favorite pastor and the main Church. The dispute brings about a schism, and the pastor forms a new sect, bringing his congregation with him. While this may not make headlines, the entire town will be abuzz with debate over which church is right. Families may even split apart due to this "innovation."
For example, there's the story of the "Navelites" who believe that Adam and Eve did not have navels, and that that particular belief has profound enough implications to justify forming a new sect.
Maybe innovation is not the right word, since that implies progress. For these people, the goal is to look to the past and remove corruptions in Christianity, thereby making it more pure and conservative.