However, if you strip down the definition to its bare essence — “a Catholic who believes the Chair of Peter at this moment is vacant”, or even “a Catholic who believes that the status of the Chair of Peter at this moment is something other than it actually is” — then it’s hard to see how this places the person outside the Church.
That would fall under the second category, “a Catholic who believes that the status of the Chair of Peter at this moment is something other than it actually is”.
To use a
reductio ad absurdum, a priest wakes up in the morning and has not yet heard the news that the pope died during the night. He goes to the Church and offers Mass
“una cum” the dead pope. He "believes that the status of the Chair of Peter at this moment is something other than it actually is”. Or the other way around — the pope has died a few days prior, the cardinals are in conclave, and a new pope has been elected during the night. He hasn’t heard the news yet. He does not offer Mass
“una cum” the new pope
(“una cum” is omitted during the short
sede vacante interregnums between papal elections). He is mistaken as to a point of fact, but he cannot be said to be “outside the Church” or “not Catholic”.
Again, I do not agree with any of the sedevacantist theories floating around out there, but I have my doubts that we can automatically say sedevacantists are “not Catholic”.