Is it necessary to be Catholic to be saved?

I. "Catholic"
II. Who is Catholic?
III. What are the true teachings of the Catholic Faith?
IV. Is it necessary to be Catholic to be saved?
V. Can the Church’s Dogmatic teaching change?
VI. What must we do to be truly called Catholic?
 

Many Catholics today object to, or even outright reject, the teaching of “Extra Ecclesiam nulla salus” or “No salvation outside the Church”.  This is very dangerous, however, because this is a defined Dogma of our Catholic faith which we must believe or we cannot be saved. (Fundamentals of Catholic Dogma, Dr. Ludwig Ott, pgs. 312-13)  The following are the official pronouncements through the history of the Church, and for which I have provide complete citations including the paragraph number where it can be found in Denziger’s The Sources of Catholic Dogma:

"By heart we believe and by mouth confess the one Church, not of heretics but the Holy Roman, Catholic, and Apostolic Church outside which we believe that no one is saved."

-Pope Innocent III, Eius exemplo, 18 December 1208 (DS 423)

"The universal Church of the faithful is one outside of which none is saved."
-Pope Innocent III, Fourth Lateran Council, November 1215 (DS 430)

"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, Unam Sanctam, 18 November 1302 (DS 468)

“No man of the wayfarers outside the faith of this Church, and outside the obedience of the Pope of Rome, can finally be saved.”

-Pope Clement VI, Super quibusdam, 20 September 1351 (DS 570 b)

"The Most Holy Roman Church firmly believes, professes and proclaims that all those who are outside the catholic church, not only pagans but also Jews or heretics and schismatics, cannot share in eternal life and will go “into the everlasting fire which was prepared for the devil and his angels” [Matt. 25:41], unless they are joined to the catholic church before the end of their lives; that the unity of the ecclesiastical body is of such importance that only for those who abide in it do the church's sacraments contribute to salvation and do fasts, almsgiving and other works of piety and practices of the Christian militia produce eternal rewards; and that nobody can be saved, no matter how much he has given away in alms and even if he has shed his blood in the name of Christ, unless he has persevered in the bosom and the unity of the catholic church.”
-Pope Eugene IV, Council of Florence, Bull Cantate Domino, 4 February 1441 (DS 714)

“Likewise, all other things I accept and profess, which the Holy Roman Church accepts and professes, and I likewise condemn, reject, and anathematize, at the same time all contrary things, both schisms and heresies, which have been condemned, rejected, and anathematized by the same Church. In addition, I promise and swear true obedience to the Roman Pontiff, the successor of Blessed Peter, the prince of the Apostles and the vicar of Jesus Christ. And that this faith of the Catholic Church, without which no one can be saved, etc. . . . [as in the Tridentine profession of faith].”

-Pope Benedict XIV, Nuper ad nos, Profession of Faith prescribed of Eastern Rite Catholics, 16 March 1743 (DS 1473)

"For, it must be held by faith that outside the Apostolic Roman Church, no one can be saved; that this is the only ark of salvation; that he who shall not have entered therein will perish in the flood; but, on the other hand, it is necessary to hold for certain that they who labor in ignorance of the true religion, if this ignorance is invincible, are not stained by any guilt in this matter in the eyes of God. Now, in truth, who would arrogate so much to himself as to mark the limits of such an ignorance, because of the nature and variety of peoples, regions, innate dispositions, and of so many other things? For, in truth, when released from these corporeal chains "we shall see God as He is" [1 John 3:2], we shall understand perfectly by how close and beautiful a bond divine mercy and justice are united; but, as long as we are on earth, weighed down by this mortal mass which blunts the soul, let us hold most firmly that, in accordance with Catholic teaching, there is "one God, one faith, one baptism" [Eph. 4:5]; it is unlawful to proceed further in inquiry. "

-Blessed Pope Pius IX, Singulari Quadem, 17 March 1856 (DS 1647)

"Here, too, our beloved sons and venerable brothers, it is again necessary to mention and censure a very grave error entrapping some Catholics who believe that it is possible to arrive at eternal salvation although living in error and alienated from the true faith and Catholic unity. Such belief is certainly opposed to Catholic teaching. There are, of course, those who are struggling with invincible ignorance about our most holy religion. Sincerely observing the natural law and its precepts inscribed by God on all hearts and ready to obey God, they live honest lives and are able to attain eternal life by the efficacious virtue of divine light and grace. Because God knows, searches and clearly understands the minds, hearts, thoughts, and nature of all, his supreme kindness and clemency do not permit anyone at all who is not guilty of deliberate sin to suffer eternal punishments. Also well known is the Catholic teaching that no one can be saved outside the Catholic Church. Eternal salvation cannot be obtained by those who oppose the authority and statements of the same Church and are stubbornly separated from the unity of the Church and also from the successor of Peter, the Roman Pontiff, to whom 'the custody of the vineyard has been committed by the Savior.'(Ecumenical Council of Chalcedon in its letter to Pope Leo)"

-Blessed Pope Pius IX, Quanto Conficiamur Moerore, 10 August 1863 (DS 1677)

"But when we consider what was actually done we find that Jesus Christ did not, in point of fact, institute a Church to embrace several communities similar in nature, but in themselves distinct, and lacking those bonds which render the Church unique and indivisible after that manner in which in the symbol of our faith we profess: 'I believe in one Church.'...For this reason Christ, speaking of the mystical edifice, mentions only one Church, which he calls His own - "I will build my church;" any other Church except this one, since it has not been founded by Christ, cannot be the true Church...The Church, therefore, is bound to communicate without stint to all men, and to transmit through all ages, the salvation effected by Jesus Christ, and the blessings flowing there from. Wherefore, by the will of its Founder, it is necessary that this Church should be one in all lands and at all times...The Church of Christ, therefore, is one and the same for ever; those who leave it depart from the will and command of Christ, the Lord - leaving the path of salvation they enter on that of perdition."

-Pope Leo XIII, Satis Cognitum, 29 June 1896 (DS 1955)

"Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed. "For in one spirit" says the Apostle, "were we all baptized into one Body, whether Jews or Gentiles, whether bond or free." [I Cor. 12:13] As therefore in the true Christian community there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith. [Eph. 4:5] And therefore if a man refuse to hear the Church let him be considered -- so the Lord commands -- as a heathen and a publican. [Matt. 18:17] It follows that those are divided in faith or government cannot be living in the unity of such a Body, nor can they be living the life of its one Divine Spirit."

-Venerable Pope Pius XII, Mystici Corporis, 29 June 1943 (DS 2286)