There is only one movement of Objectionism in the 7th Sea main rulebook or in the Eisen book (where one would logically expect to find the religion expanded). Since we're complicating Théah, let's go ahead and add back in a bunch of sects, make it a little spicier.
Amboisnots—the Reformed Church of Montaigne, Amboisnots are a Magisterial Objection sect found in Montaigne. Since the first reforms of Lieberism, the Montaignians have been struggling to find a way to cope with Amboisnots; the Edict of Chartrouse in 1610 declared Objectionism legal in Montaigne and recognized members of the Amboisnot Church as citizens of the kingdom. This was in the wake of the Tumult of Hugo, a plot conducted by Hugo du Toraine in an attempt to wrest control of the Montaigne government from the Church of the Prophets by kidnapping the young king.
Lieberism—the "main" branch of the Objection movement, Lieberism follows the teachings of Matthias Lieber and grew from his objections to the Vaticine order. Whenever "normal" Objectionists are mentioned in a 7th Sea product (as opposed to Church of Avalon folk) they are Liebers.
Hyperianism—An extreme (l'objectionist extreme) sect, Hyperianism grew from the split between Andreas Hyperius and Matthais Lieber over the divinity of the Prophets and their physical presence in the world. Hyperianism emphasizes both the Theology of the Will (voluntary union of Theus and Man) as well as the State of Predestination (all those who will be saved are predetermined to be saved). Hyperianism is primarily to be found in Northern Eisen and parts of Vendel.
Rededicants—A primarily peasant sect, very popular amongst the Eisen peasantry and parts of northern Vodacce, Rededicants believe that they must be figuratively reborn into a community of the faithful. Persecuted by both the Vaticine as well as the Magisterial Objectionists (such as Liebers), the rededicant theology focuses on mystic revelation and the ability of the individual to tap into the power of Theus and receive insight. Communities without traditional marriage or other social ties feature prominently in Rededicant faith—as does the denial of the material world as evil. This has prompted the Vaticines to label the Rededicants "Manikees," a sect that was suppressed in southern Montaigne and northern Vodacce during the Middle Ages.