To be a Catholic, is to be in communion with each other to have the same belief, the same leaders. I know that’s not the real definition.
I guess the question is can you be a catholic and be disobedient to the Church, I say no, a cafeteria catholic is not a catholic
to me.
Just because you’re not excommunicated doesn’t mean you’re a catholic, You can find none catholic’s that have had their excommunication lifted.

I agree with most of what you are stated.
Only, Dr. Williamson can not be a valid Bishop, if he was not granted permission by the Holy See, and you still call him a Bishop, I don’t understand.
For the ordination of a deacon, priest or bishop to be valid you do not need to be in communion with the pope. You need to be ordained by a valid bishop. The pope cannot take away the power of any bishop. He can forbid an ordination. But if the bishop ordains, the ordination is valid. It is illegal and the bishop is excommunicated. But the bishop who does the ordaining and the bishop who was ordained are both valid successors of the Apostles.
This is the case with the Orthodox. They were once excommunicated. But they are valid bishops, priests and deacons and all their sacraments are valid.
What exists between Bishop Williamson and the Apostolic See is a rift in protocol. There is no queston about him being a valid bishop. He was ordained illegally. But the law does not take away a bishop’s priestly powers. Therefore, a bishop can ordain, even illegally and the ordination is accepted by the Church. Because the sacrament trumps the law.
The only time when an ordination is invalid is when there is no proper matter and intention. For example, you cannot ordain a woman. The proper matter for ordination is a male. You cannot validly ordain someone who is not baptized. All the sacraments build on baptism.
If the Church were to deny that validity of this ordination she would be saying that the law trumps the power of the priesthood. A bishop posesses the fullness of the priesthood. Therefore, he can ordain another bishop, even against the wishes of the pope.
Archbishop Lefebvre and the four bishops were excommunicated because they disobeyed, not because the sacrament was invalid. The sacrament was very valid. But it was performed illegally. The law protects the sacrament. You cannot abuse the sacraments.
You know how we’re talking a lot about the sexual abuse by priests. These priests who are dismissed from the clerical state remain priests until death, unless it can be proven that their ordination was invalid.
To say that Bishop Williamson is not a bishop, one has to prove that the ordination was invalid. If we examine what do you need for a valid ordination, we see: the candidate must be baptized and male. The candidate must be a presbyter. The person doing the ordaining must be a validly ordained bishop. The candidate and the bishop who are doing the ordaining must have the intention to ordain and be ordained. Bishop Williamson meets all the canonical requirements.
What’s the big deal then? It was done without permission. But permission is not required for validity. It’s only required to make it legal. It’s illegal, but binding on the Bishop Williamson and on the pope. The pope has to accept him as an equal. Remember, the pope is a bishop. He has to accept him, just as he accepts the bishops of the Orthodox. What the pope does not have to accept is the way is was done. This is what John Paul stated and why they were excommunicated…
Pope Benedict lifted the excommunication because it did not have the desired effect. The purpose of excommunication is to bring back the sinner, not to damn him to hell. Since this did not bring these bishops back, the excommunication did not serve its purpose. So it was lifted and a new strategy is being tried. That’s what the talks between the SSPX and the Hoily See are all about.
Does this help?
Fraternally,
Br. JR, OSF
