Assuming that the SSPX has received canonical status and works for example in the dioceses of Boston, Worcester, Manchester,USA the Society of St. Pius X (SSPX) has to remove tension and clarify that Vatican Council II agrees with the dogma extra ecclesiam nulla salus. Since Ad Gentes 7 supports the dogma while LG 8 and 16 are not exceptions. If they were exceptions it would mean we can spot the dead saved in invincible ignorance etc.
They would have to assure Cardinal Sean O Malley and the other bishops that the SSPX are not ‘spotters’. They cannot see the dead.So they do not know of any exceptions to the dogma on exclusive salvation in only the Catholic Church.
Then they would have to assure the cardinal and the bishops that they fully support Vatican Council II and so cannot accept the ‘theology of religions’ or the ‘ecclesiology of communion’ since Ad Gentes 7 says all need Catholic Faith and the baptism of water for salvation.
Then they must assure the cardinal and bishops that they love all Jews and other non Catholics just as Jesus asks of them and they also believe that Jews were the People of God. Vatican Council II (Nostra Aetate 4) says that the Catholic Church is the new people of God.Catholics are now the Chosen People of God.They have the Jewish Messiah,promised by the Jewish prophets, the eternal Covenant and the Sacrifice of the Holy Mass.They have the baptism of water.
-Lionel Andrades