Traditionalist and non-traditionalist Catholics

Dominus Iesus is the document I was referring to. It was written by Benedict and issued near the end of John Paul II's reign. While it may not specifically reject the two lung theory or the 'sister church' terminology, it effectively does so by saying that there is only one Church of Christ and that it subsists in the Catholic Church. Yes, it does go on to refer to the Orthodox as 'particular churches', apparently meaning that they have valid sacraments and Apostolic Succession. However, looking at the description as the Orthodox as 'wounded' for not being in union with Peter, said document at the very least throws cold water on the two lung description of the Church of Christ.

I should add that my memory appears to have been proven to be partially in error in this matter. I thought that Benedict totally rejected the 'sister church' terminology. However, doing a quick search now, it seems that he only rejected it in regards to Protestants, since the Catholic Church does not consider them churches, but 'ecclesiastical communities', without a valid Eucharist or Apostolic Succession. While some may claim that the theoretical doctrine of two lungs to the Church of Christ is still valid, and/or the 'sister church' terminology, such is iffy at the very least. However, the fact that the Catholic Church does allow Orthodox to partake of Catholic Communion, does perhaps allow some justification for the use of the two lung/sister church terminology?

I don't think Dominus Iesus rejects the two lung theory. The "subsists in" comes right out of Lumen Gentium, and it is highly unlikely that John Paul II thought his language about "two lungs" contradicted LG or that Ratzinger thought a reiteration of LG contradicted John Paul II, who was Pope at the time of Dominus Iesus' writing. DI does not even mention Orthodoxy or even the East except to deny an easy dichotomy (logical vs symbolic).

This question requires an analysis of Ut Unum Sint. There's no two ways about it.

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After having been around the whole, Trad - Non-Trad thing and seeing all the dispute and division - in practicality Catholicism is all divided up just like protestantism. Some reject the pope, some say you should not attend Novus Ordo, some say only communion on the tongue, and the list goes on and on.

And the idea that having a pope fixes things is disproved when the current one opens his mouth.