Regarding John XXIII, most Sedevacatists are not quick to conclude that he was not a Pope. For myself, I believe John XXIII was a true Pope, but was misled. I base this on the evidence that is publicly available.
What about Paul VI?
Paul VI was a public heretic who did things that a Pope could not do, so there is a world of difference between him and John XXIII.
Do you believe Paul VI was validly elected?
I have very strong doubts that he was validly elected. I am not convinced that this man possessed the Catholic Faith, which is crucial for an election to be valid.
There are two possibilities with Paul VI, he was validly elected on June 21, 1963, and fell from his office on December 7, 1965 or that he was never Pope to begin with. For myself, I lean to the latter.
Sedevacantists are not settled on this point either. Bp. Guerard des Lauriers set the date of Paul VI's fall on December 7, 1965, the date that he approved the Vatican II docuмents. I am not sure if those who follow his thinking say the same, such as Bps. McKenna or Sanborn.
From the very beginning of his (Paul VI) "pontificate," there was turmoil in the Church on doctrinal matters. His inaction, and tacit approval of the heretics at Vatican II were a demonstration of his lack of Faith. His actions and inaction in defense of the Faith, which was under grave attack, are proofs that the man was not guarding the Sacred Deposit, rather he was allowing it to be perverted.
This demonstration of a lack of Faith, coupled with turmoil among the hierarchy on doctrinal matters, demonstrates a lack of peaceful acceptance to Paul VI. The hierarchy that was remaining faithful, clearly was not trusting Paul VI as Pope during the Council, and this was only further demonstrated by the resistance to the
Novus Ordo Missae, due to
doctrinal problems in the rite. Such acts are unheard by Catholics towards a true Pope.
The fact that members of the hierarchy were resisting Paul VI on matters of doctrine in the 1960's is a demonstration of a lack of peaceful acceptance. We are not talking about disagreements on prudential matters with the Pope, but on doctrinal matters. Catholics do not have such disagreements with the Pope, either directly or indirectly, they trust the Pope and his office which protects him.