Fact #2: Since a heretic by definition does not profess this "one faith," he cannot be a member of this "one Church." This is not merely a man-made logical conclusion; it is a dogma solemnly taught by popes, both in their ordinary and in their extraordinary magisterium. An example or two of each follows.
Ordinary magisterium: "By the heart we believe and by the mouth we confess the one Church, not of heretics, but the Holy Roman, Catholic, and Apostolic Church outside of which we believe that no one is saved" (Pope Innocent III, Eius exemplo, Dec. 18, 1208). "For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy" (Pope Pius XII, Mystici Corporis Christi, 23).
Extraordinary magisterium: "The Holy Roman Church firmly believes, professes, and preaches 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, unless they are joined to the Church before the end of their lives (Pope Eugene IV, Council of Florence, Cantate Domino, 1441; read full text in Denzinger 714).
The Sin of Heresy vs. the Crime of Heresy

Notice, by the way, that Pope Pius XII makes it clear, in the quote above from his 1943 encyclical Mystici Corporis, that it is the sin of heresy, not the crime of heresy, that "severs a man from the Body of the Church." This is a crucial distinction, for many ill-instructed Catholics erroneously claim that, until someone is found guilty of the crime of heresy by a legal proceeding (a formal admonition, followed by a heresy trial), he is still a member of the Church. This would mean that a layman or cleric (be he parish priest, bishop, or occupant of the papal see itself) who spent his entire life denying (say, in his speeches and writings), for example, the deity of Christ, the inerrancy of Sacred Scripture, the existence of hell, or the perpetual virginity of Mary, would somehow remain a member of the "one body" whose members all profess the "one faith," provided he was never formally charged with, and found guilty of, the crime of heresy, and that every faithful member of the Church would be obliged to accept such a man as a fellow Catholic. Alas for such ill-instructed “Catholics," the answer is that, yes, "one little heresy" does put you completely outside the Church. God does not grade on the curve: orthodoxy, and hence membership in the Church, is only "pass/fail." There is no such thing as being "a little bit heretical," any more than there is such a thing as being "a little bit pregnant." There's no such thing as being "99% Catholic": you either are or you aren't. It's all or nothing. As in baseball, you're either safe or you're out. Here's the proof:
The practice of the Church has always been the same, as is shown by the unanimous teaching of the Fathers, who were wont to hold as outside Catholic communion, and alien to the Church, whoever would recede in the least degree from any point of doctrine proposed by her authoritative Magisterium. (Pope Leo XIII, Satis Cognitum # 9; June 29, 1896).
Unfortunately, not only so-called conservatives but even many soi-disant traditionalists have bought the Vatican II heresy of "partial communion," which was never taught by the Catholic Church before Vatican II (nor, therefore, has it been taught by the Church since, since the Church cannot change its doctrine). The irony is that, in attempting to argue that "nearly traditional" prelates (e.g. "bishops" who generously allow the "Tridentine Mass") retain their Church membership, such people end up forfeiting their own, since they hold to a view never held by Catholics, but rather condemned by every pope (as by Pope Leo XIII in the quote immediately above).
The Ineligibility of Heretics to Hold Office in the Church ... Fact #3: It is the indisputable teaching of the Church that, if a man who falls into the sin of heresy does not retain membership in the Church, then by the selfsame fact he cannot retain whatever office he previously held in the Church, since, as Pope Leo XIII reminds us in his 1896 encyclical Satis Cognitum (paragraph 15), "it is absurd to imagine that he who is outside [the Church] can command in the Church."

Consider, too, the clear teaching of canon 188.4 in the 1917 Code of Canon Law: "Any office becomes vacant upon the fact and without any declaration by tacit resignation recognized by the law itself if a cleric publicly defects from the Catholic faith." Notice that if a man "publicly defects from the Catholic Faith" (as he does, for example, by teaching heresy), his office in the Church automatically (upon the fact; the Latin is ipso facto) becomes vacant, "without any declaration" being necessary. (So much for the imagined requirement of a formal admonition, much less a conviction at the end of a long heresy trial.) He is deemed, by his very espousal of heresy, to have "tacitly [i.e., silently] resigned" from his office, a resignation "the law itself" equally silently accepts. Done deal. Case closed. Up to and Including the Papacy Itself Notice, too, that canon 188 says any office. "Any" means "any." The highest office in the Church, the office of the papacy itself, is no exception to this immutable law of God's kingdom; on the contrary, it is precisely at the pinnacle of the Church's hierarchy that this law assumes paramount importance. The text is Gerry's above.

Think about a heretical bishop who has lost his office based on Cum Ex Apostolis Officio during the Council of Trent. Some authors would like you to believe the excommunicated bishop can ordain priests and even consecrate bishops. We know based on the Church's teaching this cannot be true, but even these sedevacantist heretics seem to think you can make valid priests and bishops and give a true Mass. The Church condemns the notion and will not permit supplied jurisdiction to heretics after Vatican II. It means the priesthood of a individual who is or becomes a heretic is held to the same standard and is defrocked by Christ Himself. So heretics can delude themselves all they want and pretend a priest cannot be stripped of given sacraments. Then what are censures, vitandi and excommunication imply? Canon Law or Divine Law cannot impose a sentence of a limited time or permanent punishment on a heretical priest! So they think the hands of God can be tied so they can SIN.

Now take a look at this statement from parts of the bull Apostolicae Curae from Leo XIII and while I do not have a problem with Leo XIII a true Pope, there is something not right about this statement. The Church never presumes anything, it is either yes or no or it either accepts or it rejects without COMPROMISE on all matters of the faith and morals in order to warn others of the eternal damnation of souls. How the devil even works manifestly through sedevacantists. You decide if you want to burn in hell by being in communion with heretics or take the safe way and don't accept them, their Mass nor the sacraments they offer you.

The Church teaches that one is presumed to have the intention of the Church unless there is clear evidence to the contrary. Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: "When anyone has rightly and seriously made use of the due form and the matter requisite for effecting or conferring the sacrament he is considered by that very fact to do what the Church does. On this principle rests the doctrine that a sacrament is truly conferred by the ministry of one who is a heretic or unbaptized, provided the Catholic rite be employed. On the other hand, if the rite be changed, with the manifest intention of introducing another rite not approved by the Church, and of rejecting what the Church does, and what by the institution of Christ belongs to the nature of the sacrament, then it is clear that not only is the necessary intention wanting to the sacrament, but that the intention is adverse to and destructive of the sacrament." Circumstantial evidence that someone might have been a Freemason is not sufficient to consider his ordinations or sacraments invalid. If one could question the intention of someone just because that person might have been a Freemason, then there would be absolute chaos in the Church. One could go back into history and start questioning all kinds of lines. For instance, Cardinal Rampolla del Tindaro was the Secretary of State under Pope Leo XIII. He was a bishop. It is widely believed that he was a Freemason, and evidence is cited by those who wish to prove it. How many people did Rampolla ordain? Has the Church gone back and re-ordained all of those men? No. That, in itself, suffices to refute the position. If the traditional rite has been used, the Church presumes that one had the intention to do as the Church does, unless the contrary is explicitly manifested.

33. With this inherent defect of "form" is joined the defect of "intention" which is equally essential to the Sacrament. The Church does not judge about the mind and intention, in so far as it is something by its nature internal; but in so far as it is manifested externally she is bound to judge concerning it. A person who has correctly and seriously used the requisite matter and form to effect and confer a sacrament is presumed for that very reason to have intended to do (intendisse) what the Church does. On this principle rests the doctrine that a Sacrament is truly conferred by the ministry of one who is a heretic or unbaptized, provided the Catholic rite be employed. On the other hand, if the rite be changed, with the manifest intention of introducing another rite not approved by the Church and of rejecting what the Church does, and what, by the institution of Christ, belongs to the nature of the Sacrament, then it is clear that not only is the necessary intention wanting to the Sacrament, but that the intention is adverse to and destructive of the Sacrament.

The text in brown is chapter 33 of the Bull Apostolicae Curae and I will give you my opinion on this. First if the statements in question that don't sound Catholic are infallible then we better believe that the Church can permit heretics to act and do things inside the Church. But do you see anywhere Leo XIII mentions anything about freemasons or communists? Were those priests validly ordained or not that are heretics or perhaps freemasons? No way and while I think those poor souls had no idea they received invalid sacraments perhaps the infinite mercy of God will not condemn them but surely I do tell you those clergy and those bishops were condemned. Rampolla burns in the darkest parts of hell as does Lienart, so ignore those who tell you that you can accept these apostates and heretics to give you valid Masses and sacraments whoever they may be including the most expert sedevacantists. The blue font has been slightly modified and I am not here to show disrespect to the writers but we dissent on this. It was not infallible that Leo XIII elevated Rampallo, who is in fact a freemason who never had the intention to do what the Church does. This shows you that the Holy Ghost did not inspire Leo to elevate an infiltrator whose goal and INTENTION was to destroy the Church from within. So the blue text is inconsistent and not compatible with what the Divine Law of a Holy and Perfect Church would demand. I said DEMAND -- "D__N" IT, it does not suggest, it does not presume, it does not infer anything that is ever slightly in opposition or contrary to its unchanging and unyielding specifications and meanings. God would allow total chaos in the Church and Christ would allow the devil to attempt to destroy the Church. So you must reject a freemason all the time and their actions inside the Church for they are null and void. One who holds no office or even a place in the Church cannot act in its behalf other than baptisms and then I would suggest never be baptized by a freemason or communist. A heretic we can deal with for the purpose of baptisms.

I do not believe the Latin translation into English is correct but even if it is what was Leo XIII thinking and not realize he contradicted Eugene IV, Trent, Cum Ex, and even his own infallible teaching in Satis Cognitum? But then in order to mislead others for whatever reason some tend to interpret the way they want to, or could these people be getting paid to lie or distort the truth or even to satisfy their own errors because they want the easy way out sometimes? There is no easy way with the true Catholic Church. But what if Leo was wrong if he indeed specified a heretic bishop or priest can validly confect sacraments and consecrate and ordain if they have the intention of the Church? Can a communist or freemason have the intention of the Church, no way? - your Catholic self says it is impossible and Divine Law will never accept a heretic, freemason or communist to act validly or licitly in the Church other than baptisms. Confession and extreme unction by a heretic is questionable. A doubtful sacrament is no sacrament at all and is grave mortal sin to accept a doubtful sacrament. Clement XIV and Benedict XIV cleared these matters up based on what Innocent XI said about doubtful sacraments where you are not allowed to guess. God would allow chaos and souls to be lost and that included most of the souls at the time of Rampolla. If God sees fit he will give the grace to souls to find the truth and if He didn't condemn the ignorant people receiving invalid sacraments at the hands of invalidly ordained clergy in those times than that is God's place and not mine.

Since the death of Pius XII we have not had a Pope for over 50 years and the argument I present regarding valid consecrations of bishops in traditional circles including sedevacantists is how can their be legitimate successors of the apostolic line since we have no Pope? The matter is one that should be answered by Divine Law. The Church does not give apostolic succession to heretics, schismatics, apostates and invalidly ordained priests. The Church cannot err or permit broken lines to function in the Mystical Body of Christ. Patrick Taylor to my knowledge believes you can pray for "Pope" Benedict XVI as his pope and Mr. Taylor also ordains in the 1963 rite. So it is one step closer to Vatican II and the novus ordites. He is no bishop, and sometimes one can wonder is this man even a true priest! Well now since the Church cannot have a part of heretics such as "Bishop" Taylor he cannot validly ordain or consecrate any man to the apostolic lines as he claims. His reconsecration for example under Thuc lines is even questionable. What I am implying is that if you accept these guys especially the non-sedevacantist bums and dogs the nice word for them then you will join them in hellfire.

Sedevacantists bishops of the CMRI and SSPV both came from the SSPX, the Church rejects such ordinations and if one was not a true priest then how does he become a true bishop, and then without a Pope to lead the Church? Christ leads the Church and there is no need for heretic bishops who really have no succession or claim to an office or authority. So they will even admit they have no authority or office in the Church. I do believe that is one of the necessary requirements for a bishop. I may refer to certain information that I agree with from the CMRI or SSPV but that does not mean you can follow them or accept them as legitimate or validly ordained. Use the materials that are Catholic but do not attend their Masses or accept their sacraments. They are certainly at least doubtful and why put your soul in danger if you are not receiving true sacraments? You must do without, the anti-christ has been able to destroy a true priesthood and for those heretics that are validly ordained such as Father McKenna, Fr. Stepanich, Campbell and others like them, do not think you can attend their Mass since they are heretics. It is not a personal problem with these men, but a matter of faith and that they have a lack of faith in the Church since they don't believe you absolutely must be baptized with water and the Holy Ghost nor even be a member of the Church to be saved. Use your Tridentine Missal of pre-1955 days if you can get one and continue to pray often. Stay away from heretics so you don't end up in the pit of fire with them.