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No, I do not think so, because they have already expressed themselves. The Superior General wrote a letter to the Holy See, published in February, and a letter to Pope Leo personally, stating that he has no intention of being separated from Rome. They acknowledge the Pope, love the Pope, and pray for the Pope during the Holy Mass. They desire to be faithful and want to educate. They want to be true sons and daughters of the Roman Church. So they love the Pope, they pray for him, and they ask Rome to consent. This is not the attitude of heretics. They explicitly stated that they do not want to establish a parallel church, but their only intention in the ordinations is that these bishops will be ordained exclusively to administer the sacraments which only bishops can administer, such as ordination in the first place, and then confirmation and the consecration of churches. This is the aim, and they have no jurisdiction.
Therefore, the Superior General is not a bishop, and this should not be mixed up with jurisdiction. Also, they do not appoint these bishops to a special region. As was the practice since the archbishop favored ordinations, these bishops simply rotated and changed their ministries in different places, not only in one place. These are all factors that sufficiently demonstrate that there is no intention at all to establish a parallel hierarchy or to separate themselves from Rome. Even Archbishop Lefebvre said it would be his greatest suffering to be separated from Rome.
However, the special situation of the Church, the unprecedented crisis of faith, and the insufficient protection of the purity and integrity of the faith and the holy liturgy are unfortunately not fully guaranteed by the Holy See. We know that there is confusion and problems with some doctrinal ambiguities in certain texts and expressions of the Second Vatican Council. This has not yet been resolved in an honest way that would demonstrate true continuity with all the preceding teaching of the Church. There are still serious doctrinal ambiguities in the Novus Ordo, and these topics must be addressed in an honest way. This will probably take time for the entire Church. Therefore, I think that the Society of Saint Pius the Tenth will give a good contribution to honestly resolving these questions together with Rome. Since Rome requires, for permission of the ordinations and for granting a canonical structure, that they previously accept all the teachings of the council and, in some way, the goodness of the Novus Ordo, this is basically the problem that they cannot accept in conscience.
At the same time, the Church during and after the council said that we must no longer name the Orthodox or the Protestants as heretics or schismatics. The expression schismatics was dropped in reference to the Orthodox. When the Holy See receives Orthodox representatives, it says that they are not called schismatics and that we are almost united. As Pope Leo said on the 25th of January at the end of the Week of Prayer for Christian Unity in Rome, addressing the Orthodox and the Protestants, we are already one. So why not say the same about the Society of Saint Pius the Tenth? Therefore, I think we must be very honest and recognize the exceptional emergency situation of the crisis in the Church and the proven and declared non-schismatic intentions of the Society of Saint Pius the Tenth in ordaining bishops.
Follow-up question: If someone is validly ordained and the Holy See declares them automatically excommunicated, how should the faithful understand this? Is it considered a publicly recognized excommunication?
Bishop Schneider: Well, concretely, the excommunication will concern only the ordaining bishops and the one ordained, no others. So only these persons. It is not up to us to judge. In some way, the Church will later judge it, and we must simply continue to pray now before the ordinations, as the Holy Father agrees. If he does not agree and issues excommunication, we will pray that the excommunication will be lifted as soon as possible. The Society of Saint Pius the Tenth may, in a generous way, through generous gestures from Rome and from the Pope, I would say even in a synodal way, be integrated at least partly.