Below is an interesting article by John Vennari. It shows the difficulty in the conversations between the Vatican and the Society of Saint Pius X.
The article shows the difficulty for the SSPX reconciling in the wider Catholic Church. Where they are clashing is not in the matter of liturgy (though there is that too), but in the realm of dogma.
From the article:
Today’s Vatican would prefer we effectively discard the infallible decree of the Council of Florence which teaches:
“The Most Holy Roman Church firmly believes, professes and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews, heretics, and schismatics can ever be partakers of eternal life, but that they are to go into the eternal fire ‘which was prepared for the devil and his angels,’ (Mt. 25:41) unless before death they are joined with her; and that so important is the unity of this Ecclesiastical Body, that only those remaining within this unity can profit from the sacraments of the Church unto salvation, and that they alone can receive an eternal recompense for their fasts, almsdeeds, and other works of Christian piety and duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved unless they abide within the bosom and unity of the Catholic Church.”
The dogma of No Salvation Outside the Church in Latin is: Extra Ecclesiam nulla salus
The article points out that the SSPX’s position is that of the Catholic Church, throughout the ages, that to be saved one must become Catholic.
The SSPX position is nothing more than the traditional teaching of the Catholic Church throughout the ages, that all non-Catholics, Jews included, must convert to the Catholic Church for salvation. There is no salvation outside the Church.
I could be wrong, but I don’t see the SSPX giving way on this. I think the Vatican is going to be disappointed if they think the SSPX is.
One Note: The article mentions both Protestants and Jews. There is a push by the Church recently to state that the original Covenant, or Old Covenant made with the Jews has never been revoked. This was first done (I think he was first) by Pope John Paul II in the Address to Representatives of the West German Jewish Community:
The first dimension of this dialogue, that is, the meeting between the people of God of the Old Covenant, never revoked by God [cf. Rom. 11:29], and that of the New Covenant, is at the same time a dialogue within our Church, that is to say, between the first and the second part of her Bible.
The Address is much longer than that. Please click the link and read it all.
I think it is a long road ahead for any reconciliation between the SSPX and Rome. I will continue to pray for all involved.