There are many Traditionalists who incorrectly believe that only ex cathedra pronouncements of the pope need to be followed or believed. Hence, when Pope Pius XII promulgated the Apostolic Constitution Munificentissimus Deus, defining the Assumption of Mary, using his charism of papal infallibility, it must be believed or else you are a heretic. (This is correct). They then assert, incorrectly, that when a pope issues a decree that is not infallible, like Pope Pius XII's encyclical Divino Afflante Spiritu (on Sacred Scripture), a true Catholic does not have to assent to it. They fail to grasp the Ordinary Magisterium of the papacy and all it implies. The purpose of this post is to set forth this teaching authority of a true pope, and the disastrous consequences which follow when it is either denied or not understood.
The Teaching Authority of the Pope
On August 12, 1950, Pope Pius XII promulgated his encyclical Humani Generis, which exposed and rejected some false opinions threatening to undermine the foundations of Catholic doctrine. His Holiness asked the great Thomist and Dominican theologian, Fr. Reginald Garrigou-Lagrange, a fervent anti-Modernist, to draft the encyclical. Paragraph number 20 of that document states:
Nor must it be thought that what is expounded in Encyclical Letters does not of itself demand consent, since in writing such Letters the Popes do not exercise the supreme power of their Teaching Authority. For these matters are taught with the ordinary teaching authority, of which it is true to say: "He who heareth you, heareth me"; and generally what is expounded and inculcated in Encyclical Letters already for other reasons appertains to Catholic doctrine. But if the Supreme Pontiffs in their official documents purposely pass judgment on a matter up to that time under dispute, it is obvious that that matter, according to the mind and will of the Pontiffs, cannot be any longer considered a question open to discussion among theologians.
This paragraph brings forth great theological truths. I will condense the commentary on these truths as written by theologian Fenton.
1. The teachings of the pope are not to be minimized based on the subterfuge that he is not exercising the fullness of his authority.
The teachings of the encyclicals posits an assensum per se (an assent by its very nature), because it is a teaching of the supreme doctrinal authority within the One True Church of Christ. Catholics are bound to give, not merely a polite acknowledgement, but a genuine and sincere acceptance, to the teachings which the pope sets forth with a theological qualification less than de fide (of faith--infallible) or even doctrina certa (certain doctrine).
Humani Generis thus reasserts the right of the Supreme Pontiff to command "opinionative"assent. When in his encyclicals, or in any other documents or utterances of his doctrinal office, he imposes a teaching upon the members of the Church with anything less than his supreme authority (i.e., as infallible), the faithful must accept his opinionative judgement as their own. The obligation to assent is not satisfied when a person merely allows that a teaching set forth in a non-infallible papal pronouncement is a "respectable opinion." Catholics are bound, guided by the teaching authority of Christ which comes to them in the declarations of His Vicar on Earth, to take that opinion as their own.
The day may come when an opinion of this kind needs to be modified. The Church Herself allows for this possibility by not proclaiming it as definitive and binding for all time. The holding of this opinion will possibly be seen as no longer necessary for the purity of the faith. The labors of the approved theologians will, in large part, be responsible for this development. The modifications of these declarations, when and if such modification ever comes, in no way violates the infallibility or Indefectibility of the Church since the doctrine in question was never presented as infallible and irreformable teaching.
2. The pope also teaches in a universal and ordinary manner; encyclicals are always based largely on assertions that have been taught by the Magisterium (in one form or another) before.
The First Vatican Council infallibly defined that a dogma of the faith is a truth which the Church finds contained in either of the two sources of Revelation (Holy Scripture and Sacred Tradition) and which She presents as divine revelation that all must accept as such. The Council goes on to explain that such presentation may be done in an extraordinary manner (infallible definitions of popes and ecumenical councils), or in a universal and ordinary way (the unanimous teachings of the approved theologians or teachings of the bishops spread throughout the world).
Vatican Council I also presents as dogmatic the assertion that the pope enjoys the same infallibility in defining dogma that the universal Church possesses. Since the bishops can define a dogma in an extraordinary way (ecumenical council called and approved by the pope), or in a universal and ordinary way (when approving theology manuals and catechisms, etc.), it follows that the pope can also teach in an extraordinary manner (ex cathedra pronouncements like the Immaculate Conception, Assumption, canonizations, etc.), he can also do so in an ordinary way, as in an encyclical letter. The pope's teaching is truly universal because he exercises true episcopal jurisdiction over each of the faithful. Many theologians consider the papal bull Apostolicae Curae of Pope Leo XIII, declaring Anglican Orders "absolutely null and utterly void," to be in this category of a dogmatic pronouncement.
3. When the pope passes judgment on a disputed theological point, it is no longer up for debate and discussion among theologians. This is one (but not the only) sign that the pope has exercised his supreme authority in an ordinary manner.
An example of this is the encyclical Mystici Corporis of Pope Pius XII. The question was disputed as to whether bishops receive their episcopal jurisdiction immediately from Christ, or from Our Lord through the Roman Pontiff, in such a way that it comes immediately through the pope. A large number of prominent theologians taught that the jurisdiction came immediately from Christ; the majority of theologians taught that it came through the Supreme Pontiff. Pope Pius XII settled the question in favor of jurisdiction coming through the pope. Another example is the Apostolic Constitution Sacramentum Ordinis also promulgated by Pope Pius XII, who settled long standing controversies over exactly what constituted the necessary and proper matter and form for Holy Orders when ordaining/consecrating deacons, priests, and bishops.
N.B. The above section was condensed from theologian Fenton, The Church of Christ, Cluny Media,  reprint of 1951 "Humani Generis and the Holy Father's Ordinary Magisterium" pgs. 110-123.
Problems for "Recognize and Resistors"
Given the above, how can the Society of St. Pius X (SSPX) refuse to submit to the following teachings of "Pope" "Saint" John Paul II in his encyclical Ut Unam Sint (all emphasis is mine).
Today we speak of "other Christians", "others who have received Baptism", and "Christians of other Communities". The Directory for the Application of Principles and Norms on Ecumenism refers to the Communities to which these Christians belong as "Churches and Ecclesial Communities that are not in full communion with the Catholic Church".This broadening of vocabulary is indicative of a significant change in attitudes. There is an increased awareness that we all belong to Christ. (para. # 42)
Problematic, as they must give their assent. Yet, how can they assent to an encyclical that teaches an ecclesiology completely opposed to what the Church taught pre-Vatican II? Consider:
And here it seems opportune to expound and to refute a certain false opinion...They add that the Church in itself, or of its nature, is divided into sections; that is to say, that it is made up of several churches or distinct communities, which still remain separate, and although having certain articles of doctrine in common, nevertheless disagree concerning the remainder; that these all enjoy the same rights; and that the Church was one and unique from, at the most, the apostolic age until the first Ecumenical Councils. Controversies therefore, they say, and longstanding differences of opinion which keep asunder till the present day the members of the Christian family, must be entirely put aside, and from the remaining doctrines a common form of faith drawn up and proposed for belief, and in the profession of which all may not only know but feel that they are brothers. The manifold churches or communities, if united in some kind of universal federation, would then be in a position to oppose strongly and with success the progress of irreligion. (Pope Pius XI, Mortalium Animos, para. #7)
Those who acknowledge Christ must acknowledge Him wholly and entirely. "The Head and the body are Christ wholly and entirely. The Head is the only-begotten son of God, the body is His Church; the bridegroom and the bride, two in one flesh. All who dissent from the Scriptures concerning Christ, although they may be found in all places in which the Church is found, are not in the Church; and again all those who agree with the Scriptures concerning the Head, and do not communicate in the unity of the Church, are not in the Church"(Pope Leo XIII, Satis Cognitum, para. # 16).
Remember, an encyclical is made up of assertions, most of which were previously taught by the Magisterium. Not so in this case, which is one of many such examples. Ut Unam Sint, clearly contradicts all that has gone before. Yet, if your recognize the post-V2 "popes," you must assent to the teachings of Ut Unam Sint. The SSPX rejects how the Church teaches us.
Problems for Feeneyites
In his encyclical Quanto Conficiamur Moerore, Pope Pius IX declares in para. #7:
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.
In the first part I emphasized, Pope Pius IX clearly states the dogma Extra Ecclesiam Nulla Salus (Outside The Church No Salvation). In the next part, he acknowledges that those invincibly ignorant, who live honest lives according to the Natural Law, and are open to the actual graces of God can be saved, not by baptism of water--or he would have written it--but "by the efficacious virtue of divine light and grace." God can infuse them with sanctifying grace and the True Faith before death (Baptism of Desire). "But it's only an encyclical, it's not infallible," the Feeneyites inevitably whine. As we see above, true assent must be given to encyclicals, but Feeneyites reject how the Church teaches us.
When Traditionalists reject (or are in ignorance of) how the Church teaches us, error will inevitably follow. Non-infallible decisions of the pope are not "up for grabs" opinions that you can accept or reject at will. Those of the SSPX (and other R&R) reject this and wind up being pulled towards joining the Vatican II sect and losing the Faith. Feeneyites will accept only infallible decrees, and their own interpretation of them, to deny the doctrine of Baptism of Desire.
In this time of the Great Apostasy, those of us who learn and accept the way the Church teaches us--- and we alone--- can hope to remain Catholic by God's grace. " But he that shall persevere to the end, he shall be saved." (St. Matthew 24:13).