Neither John Paul II, nor Benedict XVI, nor the current Pope Francis have succeeded in reuniting the Lefebvrians to Rome. The Society of St. Pius X, founded by traditionalist Bishop Marcel Lefebvre, has rejected the Pope's proposal to regularize their situation.
The superiors of the priestly fraternity have just responded negatively to the Vatican proposal to transform into a personal prelature, and did so with an arrogant tone that included insults directed at Pope Francis.
They say that "the Society of Saint Pius X does not seek primarily a canonical recognition, to which it has a right as a Catholic work.” They continued saying their mission is the "restoration of all things in Christ” and that "cannot happen without the support of a Pope who concretely favors the return to Sacred Tradition.” Additionally, they said "the proclamation of Catholic doctrine requires the denunciation of errors that have made their way into it and are unfortunately encouraged by a large number of pastors, including the Pope himself.”
Commonly called "Lefebvrians," they belong to a traditionalist movement founded in 1970 by one of the more aggressive critics of Vatican II, French Archbishop Marcel Lefebvre. In 1988, he decided to ordain four bishops, despite the expressed prohibition of John Paul II.
He justified the action by appealing to the "necessity, given the crisis of the Church;" and as a result, John Paul II excommunicated him.
In 2009, Benedict XVI withdrew the excommunication as a gesture of goodwill to facilitate reconciliation, but as they insist on rejecting Vatican II and much of the subsequent Magisterium, the situation of the group leaders within the Catholic Church remains irregular.
According to data from 2014, the fraternity has 589 priests in 37 countries, but performs activities in another 33.
Despite their demonstrated devotion and liturgical delicacy, many of their gestures show that they are, in fact, separated from Rome. They continue to believe they, and not the Pope, are the deciding factor of what and whom is Catholic and whom isn't.