I have to say, you fulfill your Sunday obligation, and it is truly not a sin to go to Holy Mass celebrated by a priest from the Society of St. Pius X. According to a document from Ecclesia Dei a few years ago, you can (only in exceptional cases) fulfill your Sunday obligation by attending a Mass of the Society of St. Pius X. There is always a Traditional Latin Mass celebrated by the Society of St. Pius X if there isn't one in your area. However, the canonical status of the SSPX is in a difficult situation.
The origin of the Society of St. Pius X is closely connected to the global crisis in the Church since the Council, we must be honest about this. If Rome had not imposed upon us the Novus Ordo, which objectively has Protestant influences, there would not have been a Society of St. Pius X with canonical irregularities. The guilt lies more on the side of Rome than on the side of Monsignor Lefebvre or the Society itself. It is evident that Rome started to do these things: the ambiguous teachings in the New Mass, which undermine the authentic doctrine of the Eucharist. No one can simply deny this. Therefore, we have to view the Society of St. Pius X in the broader context of the unprecedented doctrinal and liturgical crisis in the Church, which we have been living through since the Second Vatican Council.
Of course, the New Mass is not bad in itself; that would be an exaggeration, which unfortunately some members of the Society of St. Pius X think. The New Mass is not sacrilegious, but it has doctrinal inconsistencies. I would not conclude it to be evil, and we should refrain from saying this.
However, many celebrations of the Novus Ordo are sometimes sacrilegious, but they should not be generalized as completely evil. I, myself, celebrate the New Mass, so I do not celebrate a sacrilegious Mass, and neither do other good priests. So, we must exercise caution here.
In general, the canonical situation of the Society of St. Pius X has significantly improved as a result of the Pope granting them the authority to hear confessions and administer the Sacrament of Holy Matrimony. As a result, it is gradually making progress toward canonical status.
Dear visitors of Gloria Dei and all who have already written or who will write a personal message to me. I am grateful for your attention, your kindness, for your spiritual support and especially for your sacrifices and prayers for me. God may reward you!
