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Well, there are no schismatic intentions if society continues to act in this way. If the society does not name the Pope in the Mass and does not name the local bishop in the Mass, then one cannot assist at such Masses. But as long as they mention the Pope and recognize the Pope and the local bishop, and their only aim is to keep the faith exactly as it was until the council throughout all the centuries in the Mass, and nothing more, then they do not introduce novelties in doctrine. They do not establish their own magisterium because they simply observe the magisterium that the Church and the Popes taught over the centuries, and they follow it, not their own magisterium. They also do not completely reject the Second Vatican Council, as Archbishop Lefebvre did not. He made three important distinctions, and I think this is the same attitude of the current society.
Regarding the council, they accept it, of course, as a legitimate council, and they accept all the affirmations in which the Second Vatican Council confirmed the definitive teachings and dogmas of the Church. There are many texts and affirmations of the council that quote the dogmas and definitive teachings of the Church. For example, the Second Vatican Council taught that the episcopacy has a sacramental character, and the diaconate as well. I think society also accepts this, because before the council, throughout the centuries, this was the most common teaching of traditional theologians, even though the magisterium had not explicitly pronounced itself on the sacramental character of diaconal and episcopal ordinations. This was clarified by the Second Vatican Council, and the society accepts this and other sound teachings.
The second distinction made by Archbishop Lefebvre concerns ambiguous affirmations. Regarding these, if they can be honestly interpreted in a traditional sense and in the light of tradition, then this can be accepted. The third distinction concerns expressions that are so ambiguous that they cannot remain as they are and be accepted, or that are in themselves erroneous, not heretical but erroneous. The society says that these cannot be accepted unless they are clarified and corrected in a clear way, without any doubt, by the Church. This has not yet been done. The so-called hermeneutic of continuity is not convincing in some cases, especially regarding certain clearly ambiguous texts of the council. So we must hope that, with the help of society and other theologians, this will be clarified in the future. The magisterium and the Pope will address this in time, and we hope it will be done soon.
In this sense, I think the faithful will not sin when they participate in these Masses of the society, even after the consecrations, as I repeat, as long as they observe all the norms of the Church, namely, to mention the Pope and the local bishop, to pray for him, and to desire the clarification of these points.