Note: Vatican Council II and the Catechism of the Catholic Church refer to particular cases and not giving of the Eucharist in general.In general non Catholics are not given the Eucharist by the Catholic Church.
The understanding of Vatican Council II by the Most Holy Family Monastery is the same as that of the liberals and the Left.
They still consider the baptism of desire as a visible and known exception to the dogma extra ecclesiam nulla salus so they reject the baptism of desire! . They contradict the Council of Trent. They do not consider this a heresy. Similarly they assume that Nostra Aetate 3 refers to known exceptions to the traditional teaching on other religions.
They end up rejecting Vatican Council II and going into sedevacantism, when the fault is with their irrational interpretation of the Council.
Like the Vatican Curia and the traditionalists they are using Cushingism with the visible- dead theory in the interpretation of the Council. Without this false premise, NA 3, LG 16 etc, would not contradict Ad Gentes 7. Vatican Council II affrms the dogma extra ecclesiam nulla salus in Ad Gentes 7 and Lumen Gentium 14. They never mention Ad Gentes 7 in their books and videos on extra ecclesiam nulla salus.