Here’s the letter from the Holy Office which addressed the Fr. Feeney issues.
http://matt1618.freeyellow.com/appendixe.html
As I understand it, in a nutshell there is no salvation outside the Catholic Church because the Catholic Church is that communion of faith and charity, and without those, one cannot be saved. It is possible for faith and charity to exist outside the visibly delineated Church. Also, while there is no salvation outside the Church, everyone is given the means of partaking of that salvation.
Faith properly orders our relationship to God: "By faith, man completely submits his intellect and his will to God. (CCC 143).
Because of this, faith is necessary for salvation:
CCC
161 Believing in Jesus Christ and in the One who sent him for our salvation is necessary for obtaining that salvation.42 "Since “without faith it is impossible to please [God]” and to attain to the fellowship of his sons, therefore without faith no one has ever attained justification, nor will anyone obtain eternal life ‘But he who endures to the end.’"43
Faith is “a free assent to the whole truth that God has revealed.” (CCC 150). In particular, this means faith in Christ, since Christ “is the Father’s one, perfect and unsurpassable Word. In him he has said everything; there will be no other word than this one” (CCC 65); “what he spoke before to the prophets in parts, he has now spoken all at once by giving us the All Who is His Son” (CCC 65, quoting St. John of the Cross).
Even if in good conscience, people in non-Christian religions cannot have faith–they simply do not believe what God has revealed. Their belief is merely “religious experience still in search of the absolute truth and still lacking assent to God who reveals himself” and therefore “the distinction between theological faith and belief in the other religions, must be firmly held.” (Dominus Iesus 7).
Since they lack faith, persons who remain in such a situation until death could not be saved. However, we do acknowledge that, for those in good conscience seeking to follow the truth, “in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him.” (CCC 848)
But even if one has faith in Christ, deliberately denying any revealed truth (heresy–a sin of separation from the Church) destroys faith altogether, since one is no longer assenting to God the revealer, but trusting one’s own judgment: “Since faith is one, it must be professed in all its purity and integrity.” (Lumen Fidei 48). On the flip side, because faith is one, if one has faith in Christ–who is the fullness of revelation–faith is not destroyed by innocent ignorance about the various articles of faith: “there is no difference in the faith of ‘those able to discourse of it at length’ and ‘those who speak but little’, between the greater and the less: the first cannot increase the faith, nor the second diminish it.” (Lumen Fidei 47, quoting St. Irenaeus).