The Catechism and Vatican Council II are Feeneyite if you avoid the false premise

Feeneyism holds the literal and traditional interpretationa of the dogma extra ecclesiam nulla salus which the Catholic Church  has not retracted. Feeneyism rejects a visible to us baptism of desire and being saved in invincible ignorance.So there are no defacto exceptions to all needing the baptism of water. It means in Heaven there are only Catholics .They are are there with Catholic Faith and the baptism of water and without mortal sin.

This is also the teaching of the Catechism of the Catholic Church and Vatican Council II if you are careful to avoid the false premise i.e the premise of the dead being  visible in 2014 who are  exceptions to extra ecclesiam nulla salus.

Catechism of the Catholic Church

Feeneyism:

"Outside the Church there is no salvation"

846 How are we to understand this affirmation, often repeated by the Church Fathers?³³⁵ Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:

Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. 

 With the False premise :

CCC 846.Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.( and these cases are known to us in 2014 and so contradict CCC 846 above)

With the False premise :

847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church ( and are known to us in 2014 and so contradict CCC 846):

Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience ( and who are visible and personally known to us in 2014)- those too may achieve eternal salvation.

With the False premise :

848 "Although 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.( and who are visible and personally known to us in 2014)  

Without the false premise:

Eliminate the part in red type, the irrational premise, and CCC 847-848 do not contradict Feeneyism in the Catechism of the Catholic Church i.e 846.

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Feeneyism

VI. THE NECESSITY OF BAPTISM

1257 The Lord himself affirms that Baptism is necessary for salvation. He also commands his disciples to proclaim the Gospel to all nations and to baptize them.

False premise:

Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament.( and we personally know in 2014 these persons who are saved as such in Heaven and so they are explicit exceptions to the above part of CCC 1257.They contradict Feeneyism.)

Feeneyism:

 (CCC 1257) The Church does not know of any means other than Baptism that assures entry into eternal beatitude; this is why she takes care not to neglect the mission she has received from the Lord to see that all who can be baptized are "reborn of water and the Spirit." 

Feeneyism:

(CCC1257) God has bound salvation to the sacrament of Baptism,...

False Premise:

(CCC1257) but he himself is not bound by his sacraments (since in 2014 thee are visible for us cases of non Catholics saved outside the Church i.e without the baptism of water and Catholic Faith)

False Premise:

1258 The Church has always held the firm conviction that those who suffer death for the sake of the faith without having received Baptism are baptized by their death for and with Christ. This Baptism of blood, like the desire for Baptism, brings about the fruits of Baptism without being a sacrament ( and these cases are personally known to us in 2014 . They are not hypothetical cases and so they contradict Feeneyism in CCC 1257).

1259 For catechumens who die before their Baptism, their explicit desire to receive it, together with repentance for their sins, and charity, assures them the salvation that they were not able to receive through the sacrament.( and these cases are personally known to us in 2014 . They are not hypothetical cases and so they contradict Feeneyism in CCC 1257).

1260 "Since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partakers, in a way known to God, of the Paschal mystery."⁶³ Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.( and these cases are personally known to us in 2014 . They are not hypothetical cases and so they contradict Feeneyism in CCC 1257).

Without the False Premise:

1257.Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament.(Reason tells us that these cases are invisible for us and known only to God)

CCC1257) but he himself is not bound by his sacraments (Reason tells us that these cases are invisible for us and known only to God)

1258 The Church has always held the firm conviction that those who suffer death for the sake of the faith without having received Baptism are baptized by their death for and with Christ. This Baptism of blood, like the desire for Baptism, brings about the fruits of Baptism without being a sacrament (Reason tells us that these cases are invisible for us and known only to God)

1259 For catechumens who die before their Baptism, their explicit desire to receive it, together with repentance for their sins, and charity, assures them the salvation that they were not able to receive through the sacrament.(Reason tells us that these cases are invisible for us and known only to God)

1260 "Since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partakers, in a way known to God, of the Paschal mystery."⁶³ Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.(Reason tells us that these cases are invisible for us and known only to God)

 

Feeneyism

CCC 845 To reunite all his children, scattered and led astray by sin, the Father willed to call the whole of humanity together into his Son's Church. The Church is the place where humanity must rediscover its unity and salvation. The Church is "the world reconciled." She is that bark which "in the full sail of the Lord's cross, by the breath of the Holy Spirit, navigates safely in this world." According to another image dear to the Church Fathers, she is prefigured by Noah's ark, which alone saves from the flood.

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Vatican Council II 

Feeneyism:

Ad Gentes 7: Therefore, all must be converted to Him, made known by the Church's preaching, and all must be incorporated into Him by baptism and into the Church which is His body. For Christ Himself "by stressing in express language the necessity of faith and baptism (cf. Mark 16:16; John 3:5), at the same time confirmed the necessity of the

Church, into which men enter by baptism, as by a door. 

False premise:

Ad Gentes 7 : Therefore those men cannot be saved, who though aware that God, through Jesus Christ founded the Church as something necessary, still do not wish to enter into it, or to persevere in it.(these cases being kown to us in 2014)

False premise:

Ad Gentes 7 :Therefore though God in ways known to Himself can lead those inculpably ignorant of the Gospel to find that faith without which it is impossible to please Him (Heb. 11:6)(and these cases are known to us in 2014)...

Without the False premise:

Ad Gentes 7 : Therefore those men cannot be saved, who though aware that God, through Jesus Christ founded the Church as something necessary, still do not wish to enter into it, or to persevere in it.(Reason tells us that these cases are known only to God and so this passage is not an exception to Feeneyism )

Without the false  premise:

 

Ad Gentes 7 :Therefore though God in ways known to Himself can lead those inculpably ignorant of the Gospel to find that faith without which it is impossible to please Him (Heb. 11:6)(Reason tells us that these cases are known only to God and so this passage is not an exception to Feeneyism ).

 

Similarly Lumen Gentium 8 and 16, Unitatis Redintigratio 3, Nostra Aetate 2 etc are not exceptions to Feeneyism.-Lionel Andrades