Did you notice that the Holy Father affirmed extra ecclesiam nulla salus at the same time he set about limiting and ultimately extinguishing the Traditional Latin Mass? In his Letter to the Bishops accompanying Traditionis Custodes, Pope Francis wrote, “to remain in the Church not only ‘with the body’ but also ‘with the heart’ is a condition for salvation.”
The internal quoted material in that passage comes from an anti-Donatist work of Saint Augustine, which was itself quoted in the Vatican II (Lumen Gentium, chap. 2, par. 14): On Baptism, Against the Donatists, Book V, chap. 28, par. 39 (the last paragraph of that linked page).
As good is it is to see an affirmation of the necessity of the Church for salvation, the larger context is disturbing:
In defense of the unity of the Body of Christ, I am constrained to revoke the faculty granted by my Predecessors [to offer the TLM]. The distorted use that has been made of this faculty is contrary to the intentions that led to granting the freedom to celebrate the Mass with the Missale Romanum of 1962. Because “liturgical celebrations are not private actions, but celebrations of the Church, which is the sacrament of unity”,  they must be carried out in communion with the Church. Vatican Council II, while it reaffirmed the external bonds of incorporation in the Church — the profession of faith, the sacraments, of communion — affirmed with St. Augustine that to remain in the Church not only “with the body” but also “with the heart” is a condition for salvation. 
Implicit in that passage is the terrifying notion that the Roman Church’s own liturgical tradition bears within it the seeds of schism. Such logic not only constitutes an unthinkable attack on the Church’s own sacred patrimony; it also affirms the argument of those who say that the new Mass of Paul VI is the lex orandi of an alien religion. And this in a document whose stated purpose is to build up ecclesial unity.
The former Cardinal Prefect of the CDF, Cardinal Gerhard Mueller, thinks that the use of the passage from Saint Augustine was inappropriately twisted for use in the Holy Father’s letter:
The quotation from St. Augustine about membership in the Church “according to the body” and “according to the heart” (Lumen Gentium 14) refers to the full Church membership of the Catholic faith. It consists in the visible incorporation into the body of Christ (creedal, sacramental, ecclesiastical-hierarchical communion) as well as in the union of the heart, i.e. in the Holy Spirit. What this means, however, is not obedience to the pope and the bishops in the discipline of the sacraments [which is the meaning Pope Francis attaches to it in his letter], but sanctifying grace, which fully involves us in the invisible Church as communion with the Triune God [underlined emphasis mine, as was the explanatory bracketed comment].
Cardinal Mueller is not alone among bishops and cardinals in being openly critical of Pope Francis’ July 16 documents. He is joined by Cardinal Zen, Cardinal Burke, Bishop Athanasius Schneider, and the Dutch Bishop, Rob Mutsaerts.
Cardinal Burke asks and proceeds to answer a timely and important question regarding the authority of the Supreme Pontiff:
15. But can the Roman Pontiff juridically abrogate the UA? [Usus Antiquior (the more ancient use), which is what Cardinal Burke calls the TLM throughout his document –BAM] The fullness of power (plenitudo potestatis) of the Roman Pontiff is the power necessary to defend and promote the doctrine and discipline of the Church. It is not “absolute power” which would include the power to change doctrine or to eradicate a liturgical discipline which has been alive in the Church since the time of Pope Gregory the Great and even earlier. The correct interpretation of Article 1 cannot be the denial that the UA is an ever-vital expression of “the lex orandi of the Roman Rite.” Our Lord Who gave the wonderful gift of the UA will not permit it to be eradicated from the life of the Church.
The Dutch auxiliary bishop, Bishop Rob Mutsaerts, agrees, but is more blunt:
Pope Francis is now pretending that his motu proprio belongs to the organic development of the Church, which utterly contradicts the reality. By making the Latin Mass practically impossible, he finally breaks with the age-old liturgical tradition of the Roman Catholic Church. Liturgy is not a toy of popes; it is the heritage of the Church. The Old Mass is not about nostalgia or taste. The pope should be the guardian of Tradition; the pope is a gardener, not a manufacturer. Canon law is not merely a matter of positive law; there is also such a thing as natural law and divine law, and, moreover, there is such a thing as Tradition that cannot simply be brushed aside.
Many argue in favor of the Traditional Latin Mass using Quo Primum. This is good, but let us go deeper and realize that what Pope Saint Pius V did in that document was not only positive legislation. It was the Pope using his power to guard and defend tradition, and that tradition which long preexists Quo Primum still stands even if a pope were to have the temerity to attempt an explicit abrogation of Pius V’s bull.
This posting is subject to updates if I become aware of other episcopal statements that are germane. (Suggestions of such are welcome in the comments section.)