Many Sedevacantists quote the papal bull Cum Ex Apostolatus, of Paul IV, as a legal basis for their position that the Popes after Pius XII were not legitimate Popes.
In the following quotation, the Sedevacantist Bishop, Donald Sanborn, rector of Most Holy Trinity Seminary, explains the two reasons this argument, which is used by his fellow Sedevacantists, is false: First, Cum ex Apostolatus was derogated by the 1917 Code, and hence no longer has legal force. Second, even if it were in force, it would only not apply to the recent Popes, since they are not legally recognized as heretics by the Church. Sanborn only mentions Benedict/Ratzinger by name (since it was written prior to his abdication), but the same applies to Francis and the other recent Popes.
The following is taken from Bp. Sanborn’s explanation of the Sedeprivationist Thesis of Guérard des Lauriers:
Q. Does not Cum ex apostolatus of Pope Paul IV contradict the thesis?
A. Cum ex apostolatus is an apostolic constitution, a law, made by Pope Paul IV, which says that if a pope should be a heretic, his elevation to this dignity would be null. It was made in order to ensure that no Protestant could ever become the Pope. It does not apply to the present case for two reasons. The first is that it is no longer the law. It was derogated (made obsolete) by the 1917 Code of Canon Law. The second reason, and the more important, is that even if it should for some cause still have force, it could only apply to Ratzinger if he were legally recognized as a public heretic. But, as we have seen, there is no legal condemnation of Ratzinger. Before the law of the Church he does not have the status of heretic because (1) he himself does not hold himself guilty of heresy, and (2) no legitimate superior holds him guilty of heresy. Cum ex apostolatus certainly expresses the mind of the Church with regard to heretics holding office. It makes an excellent theological argument, but it does not make a legal argument.” http://mostholytrinityseminary.org/wp-content/uploads/2019/01/Explanation-of-the-Thesis.pdf
One final point is that Bishop Sanborn’s admission that Cum ex Apostolatus is “no longer law” shows that he's well aware that it does not retain legal force simply because it is referenced in a footnote to Canon 188.4, which is another argument used by his fellow Sedevacantists. Canon Gregory Hesse teaches the same in this video.
* Fr. Coronata also explains that Cum ex Apostaolatus is null in Institutiones Iuris Canonici.
* For more a on Cum ex Apostolatus, see here.