@Tony M As for the authenticity of Francis' papacy, I agree with Bishop Schneider. Bishop Vigano has never said he does not recognize Francis. He has only said that Catholics should consider the possibility that his election could be invalid. In my humble opinion, only God can judge that. Bishop Vigano speaks of a wrong intention of Francis when he became pope. But no one can judge the intentions of another. Even in a marriage - to which Bishop Vigano compares the appointment as pope - only the person in question can say what his/her intentions were. Thereby, a marriage is a sacrament (which can be annulled) and a choice of pope is not, so the comparison does not hold up anyway.
Archbishop Jan Pawel Lenga (rightly) accused the pope of heresy in his Abu Dhabi declaration but he too does not deny the validity of his papacy. The good, old (100 years old) bishop Gracida has made many (justified) criticisms of Francis but neither has denied the validity of his papacy.
Fr. Altmann indeed denies that pope Francis is the pope. I think he makes a mistake.
Of course some laymen can be found who deny the validity, but that is with every pope (sedevacantists you call them).
Francis functions as pope, i.e. his directives are implemented by most of the bishops (see to Synod on synodality), his encyclicals are read and considered norms by many bishops. Whether he functions as he should is another matter. But he is functioning and every morning he rises as "Pope Francis."

Bishop Mutsaerts is not retired. He has been "relieved of his administrative duties" (not by the Vatican but in consultation with his own bishop) but he still functions as a bishop in his diocese through sacramental ministry. The reason for his discharge is clear when one reads his comments. There was a deep difference of view of church and faith with his bishop and this is a "modus vivendi." In the Netherlands, through his blog, he is a support for Catholics who are faithful to the tradition and faith of the Church.

@Kenjiro M. Yoshimori I recognize that you know a lot, But knowing a lot does not necessarily mean a correct judgment. For example, I think your judgment about John Paul II is below par. The fact that there is a lot wrong in the church does not mean that changes were not needed. The idealization of Pius X, XI and XII and the triumphant era of the Church at that time is another example of a one-sided judgment. Again, there are many people who "know a lot" yet "understand little."

@123 jussi en @Chat Chartreux: (The writings of) JPII are the antidote of Francis. We miss his love, his wisdom, his sanctity, his heart of a father, his humor, his openness to the Spirit, his humility, his zeal for Jesus, his great love for Mary, and so much more. Only mediocre and petty souls accuse him of possible mistakes - as far as we can judge without knowing the background to his decisions - which disappear in the great light he radiated.

Saint Augustine shared the now-famous mantra that the Church is always reforming herself — ecclesia semper reformanda est — . But he presumably had more in mind than patchy institutional change. He was referring to the Body of Christ, the People of God. So there is a reference to a Catholic authority, even a doctor of the Church, from before Vatican II. So in the good spirit of Saint Augustin we may say that "sempre reformanda" is Catholic.