There is some problem with the Council of Trent. Not everything that the Council of Trent said was infallible. It certainly did clarify some dogma and moral questions. It also made many pastoral statements. These are all being lumped together with those that are binding. In addition, because there was no unified code of canon law, trent made some laws as well. These too are often thrown into the mix.
Every pastoral statement made by a council and every law made by a council remains in force until another council or a pope changes it.
Every dogma and moral truth taught by a council remains in force forever. However, one must understand that these truths are not proper to the council. They always existed. The council simply stated them in a formal statement. There is nothing in tradition or in practice that says that these truths cannot be restated by future popes or council in different words. There is nothing in our Catholic tradition that says that truth cannot be better understood later than before.
Here is a simple example. The Apostles knew that Jesus was God and man. This is truth. However, it was not for another 400 years that this truth was explained to everyone’s satisfaction. Until Nicea, this truth was articulated in many ways and each articulation was found to be deficient. The problem was not the truth, but the language.
This is also the case with truths taught by Trent, Pius X and others before us. This is what John Henry Newman called the development of Christian doctrine. Doctrine does not change, but it’s like a morsel of corn. If you add humidity and heat, it pops and you can see the inside. Is it still the same morsel of corn? Of course it is. However, it looks different and tastes different. It has a smoother texture, which makes it easier to eat. Who wants to eat a hard grain of corn?
So, as Bl. John Newman explains, the same thing happens with doctrine as with pop corn. The same grain of truth was present in the early Church, at the Council of Trent and at Vatican II. The appearance changes as we try to find language that clearly explains what the Church believes. There is nothing wrong with this.
As far as “Eternal Rome”, I have found this to be a rather dubious expression. When I first heard it, I had no idea what they SSPX was talking about. After asking several theologians, I leaned that the term comes from literature, not from theology or ecclesiology. It doesn’t really describe the Catholic Church for a number of reasons.
First, it’s not a term that the Church has ever applied to herself.
Second, it’s a term that is offensive to the Eastern Catholics. It seems to imply that Catholicism is Roman, which it is not. The Diocese of Rome is the mother of all Catholic Churches, but the Catholic Church is not the Diocese of Rome. The Catholic Church is not even the Latin Church.
The key is not Rome, but the Bishop of Rome. If I’m faithful to “Eternal Rome” but am not in full communion with the Bishop of Rome, I’m in a rather irregular position. At the end of the day the Bishop of Rome will always be who he is and the Church will always depend on him, not on me. It is I who has to move toward him if I want to move toward the whole Church.