Donatism says the priest cannot peform his priestly ministry if he has sin. But a heretic is thrown out of the Church. I guess the thing here is, is the person thrown out of the Church or not? And who gets to decide that for sedes if there is no Pope?
the Holy See has told us that no heretic can be accepted as the valid occupant of the
Holy See (the Pope)! With the fullness of his authority, Pope Paul IV defined that anyone who
has been promoted to the Papacy as a heretic is not a true and valid pope, and that he can be
rejected as a warlock, heathen, publican and heresiarch.
Pope Paul IV, Bull Cum ex Apostolatus Officio, Feb. 15, 1559: “6. In addition, [by this Our
Constitution, which is to remain valid in perpetuity, We enact, determine, decree and
define:] that if ever at any time it shall appear that any Bishop, even if he be acting as an
Archbishop, Patriarch or Primate; or any Cardinal of the aforesaid Roman Church, or, as
has already been mentioned, any legate, or even the Roman Pontiff, prior to his
promotion or his elevation as Cardinal or Roman Pontiff, has deviated from the
Catholic Faith or fallen into some heresy:
(i) the promotion or elevation, even if it shall have been uncontested and by the
unanimous assent of all the Cardinals, shall be null, void and worthless;
(ii) it shall not be possible for it to acquire validity (nor for it to be said that it has thus
acquired validity) through the acceptance of the office, of consecration, of subsequent
authority, nor through possession of administration, nor through the putative
enthronement of a Roman Pontiff, or Veneration, or obedience accorded to such by all,
nor through the lapse of any period of time in the foregoing situation;
(iii) it shall not be held as partially legitimate in any way...
(vi) those thus promoted or elevated shall be deprived automatically, and without need
for any further declaration, of all dignity, position, honour, title, authority, office and