Vatican II ecumenical documents emphatically declare that Latin Catholics are not to convert Orthodox Catholics to Latin and vice versa. When ecumenical dialogue between the two is to be encouraged.
I don’t think Vatican 2 says that. The closest thing I can find is this comment: “If any separated Eastern Christian should, under the guidance of the grace of the Holy Spirit, join himself to the unity of Catholics, no more should be required of him than what a bare profession of the Catholic faith demands.”
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To me, that seems to praise conversion. I don’t see anything in Vatican 2 that says conversion of the Orthodox is not to be sought.
There is, however, a document called the
Balamand Declaration that was prepared by “[r]epresentatives of nine autocephalous and autonomous Orthodox Churches” and “twenty four members of the [International Theological] Commission”. It is
hosted at the Vatican website and says: “in the search for re-establishing unity there is no question of conversion of people from one Church to the other in order to ensure their salvation.” (paragraph 15) And: “Pastoral activity in the Catholic Church, Latin as well as Oriental, no longer aims at having the faithful of one Church pass over to the other; that is to say, it no longer aims at proselytizing among the Orthodox.” (paragraph 22)
Re: that document, I think the qualifications involved, such as “in order to ensure their salvation,” and “that is to say…proselytizing,” make this easier to understand for someone who believes, with Vatican 2, that conversion to Catholicism is something to be assisted. Also, it is noteworthy that the International Theological Commission is an advisory body and is not a part of the Magisterium. Thus, unless I’ve missed something, this document is a suggestion to the Congregation for the Doctrine of the Faith, and doesn’t bind our course of action.