Some common objections heard when pointing to the conclusion of sedevacantism:
"Who are you to judge the pope?"
"You're behaving like a protestant."
"You don't have the authority to declare."
Yet what does the Church say? What are we obliged to do?
Source: http://www.traditionalmass.org/issues/#c
2. Holy Scripture teaches us:
3. Objection raised: you are not allowed to judge the pope.
4. "The pope is your link to Christ. [...] It would be schismatic to submit to someone as pope who is not the pope." - Fr. Benedict Hughes, CMRI
5. Important distinction: We are never allowed to judge other people’s consciences but we must recognize the pope's formal heresy. It is theological faith that obliges us to do so.
➡️Fr. Noel Barbara, Papal Infallibility and the Crisis in the Church Today
6. "They cannot of course define it ex cathedra, but they can lawfully hold it as perverse and declare it such, warn others against it..."
- Fr. Felix Sarda Y Salvany, Liberalism is a sin
http://www.liberalismisasin.com/chapter32.htm
7. "In our day there are a lot of people who call themselves, and mean to be, traditional Roman Catholics. Yet a great many of them do not hold to the traditional Catholic understanding of the Papacy, either because they do not know it or because they unhappily accept the “Popes” after Pius XII as valid and legitimate but know that they cannot submit to them without abandoning the traditional Catholic Faith. The tragic irony in the latter case is that by denying the Catholic teaching on the Papacy, they are abandoning the Faith just as much.
[...] The following is a list of quotations from various magisterial documents that enunciate what the Catholic Church has traditionally taught about the nature, purpose, and effects of the Papacy. It is important to know and understand this teaching because it shows that affirming that a certain man is the true and legitimate Pope has consequences: A Catholic must then affirm of him everything the Catholic Church affirms of the Pope, such as what is presented below."
Read here: NovusOrdoWatch: The Catholic Teaching on the Papacy
This is a quick thread I made and is by no means exhaustive.
Helpful links:
