The early Church held the same position on this as the contemporary Church does—that is, while it is normatively necessary to be a Catholic to be saved (see CCC846; Vatican II, Lumen Gentium 14), there are exceptions, and it is possible in some circumstances for people to be saved who have not been fully initiated into the Catholic Church (CCC847).
Notice that the same Fathers who declare the normative necessity of being Catholic also declare the possibility of salvation for some who are not Catholics.
Thats not what Pope Eugene IV said right there. I’m only posting this because the ecumenism we see in the church totally goes against previous quotations from popes and councils that I am discovering on the internet. Let me post some more.
“There is but one universal Church of the faithful, outside of which no one at all is
saved.” (Pope Innocent III, Fourth Lateran Council, 1215.)
“We declare, say, define, and pronounce that it is absolutely necessary for the
salvation of every human creature to be subject to the Roman Pontiff.” (Pope
Boniface VIII, the Bull Unam Sanctum, 1302.)
Saint Cyprian (died A.D. 258): “He who has turned his back on the Church of Christ
shall not come to the rewards of Christ; he is an alien, a worldling, an enemy. You
cannot have God for your Father if you have not the Church for your mother. Our Lord
warns us when he says: ‘he that is not with Me is against Me, and he that gathereth
not with Me scattereth.’ Whosoever breaks the peace and harmony of Christ acts
against Christ; whoever gathers elsewhere than in the Catholic Church scatters the
Church of Christ.” (Unity of the Catholic Church)
Lactantius (died A.D. 310): “It is the Catholic Church alone which retains true worship.
This is the foundation of truth, this is the abode of the Faith, this is the temple of God;
into which if anyone shall not enter, or from which anyone shall go out, he is a
stranger to the hope of life and eternal salvation.” (The Divine Institutes)
Saint Augustine (died A.D. 430): “No man can find salvation except in the Catholic
Church. Outside the Catholic Church one can have everything except salvation. One
can have honor, one can have the sacraments, one can sing alleluia, one can answer
amen, one can have faith in the name of the Father and of the Son and of the Holy
Ghost, and preach it too, but never can one find salvation except in the Catholic
Church.” (Sermo ad Caesariensis Ecclesiae plebem)
Saint Fulgentius (died A.D. 533): “Most firmly hold and never doubt that not only
pagans, but also all Jews, all heretics, and all schismatics who finish this life outside
of the Catholic Church, will go into the eternal fire prepared for the devil and his
angels.” (Enchriridion Patristicum)
Pope Pelagius II (A.D. 578-590): “Consider the fact that whoever has not been in the
peace and unity of the Church cannot have the Lord. Although given over to flames
and fires, they burn, or, thrown to wild beasts, they lay down their lives, there will not
be for them that crown of faith but the punishment of faithlessness. Such a one can
be slain, he cannot be crowned. If slain outside the Church, he cannot attain the
rewards of the Church.” (Denzinger 246-247)
Pope Saint Gregory the Great (A.D. 590-604): “Now the holy Church universal
proclaims that God cannot be truly worshipped saving within herself, asserting that all
they that are without her shall never be saved.” (Moralia)
Saint Thomas Aquinas (died A.D. 1274): “There is no enterning into salvation outside
the Church, just as in the time of the deluge there was none outside the ark, which
denotes the Church.” (Summa Theologiae)
Saint Peter Canisius (died A.D. 1597): “Outside of this communion - as outside the
ark on Noah - there is absolutely no salvation for mortals: not for Jews or pagans who
never recieved the faith of the Church, nor for heretics who, having recieved it,
corrupted it; neither for the excommunicated or those who for any other serious cause
deserve to be put away and separated from the body of the Church like pernicious
members…for the rule of Cyprian and Augustine is certain: he will not have God for
his Father who would not have the Church for his mother.” (Cathechismi Latini et
Germanici)