No, for the Society of Saint Pius X have canonical irregularities. To be clear, the Society of Saint Pius X is neither a schismatic organization and is not separate from the Church.
Only 4 Bishops were consecrated without the permission of the Pope, and they were excommunicated by Rome as a punishment. However, Pope Benedict XVI lifted their excommunication in 2009.
Pope Francis granted the SSPX faculties in Confession despite their canonical irregularities. So how can Rome permit the SSPX to lawfully hear confessions if Rome considers the SSPX to be outside the Church? While the Holy Mass of the SSPX have always been seen as valid, though of questionable liceity, other sacraments especially Holy Matrimony remains doubtful. Fortunately, Rome granted conditional faculties to priests in their dioceses to celebrate the Nuptial Mass.
Given their current predicament, the SSPX's existence is connected to the extraordinary crisis facing the Church. After the Council, they arose as a result of the necessity to resist modernity within the Church. We can contrast this crisis historically with the early Church's battle with Arianism. When the Aryans infiltrated the Church and St. Athanasius was excommunicated, he remarked, "They may have taken our churches, but we have the faith; they may have the building and the canonical structure, but not the faith."
Therefore, in the case of the SSPX, we must consider the larger perspective, earnestly pray that the SSPX may one day be granted regular canonical status, and continue to pray for the communities that are making an effort to uphold the faith.
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