Actually Catholics think the Orthodox are members of the Church by virtue of baptism, apostolic succession, and the Eucharist. They are separated from us in some ways, unified in others. In fact, Orthodox are permitted to receive the Eucharist in a Catholic church in some circumstances, and Catholics can receive in an Orthodox liturgy in some circumstances (according to the Catholic Church, anyway).
Edit (CIC 884):
“§2. Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-
Catholic ministers in whose Churches these sacraments are valid.
§3. Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches.”
Not so! The Catholic Church teaches that she alone is the unique
Church of Christ, and that all other religions, whether Christian or non-Christian, are sects. They are false religions. St. Cyprian said, "There is one God, and Christ is one, and there is one Church and one chair founded upon the rock by the word of the Lord. Another altar cannot be constituted nor a new priesthood be made except the one altar and the one priesthood. Whosoever gathereth elsewhere, scattereth.”
The Church teaches that those people are members of the Catholic Church who have been validly baptized, and who have not been excluded from the Catholic Church by means of heresy, schism, or excommunication. Pope Pius XII teaches in his encyclical “Mystici Corporis”:
"Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed. 'For in one spirit' says the Apostle, 'were we all baptized into one Body, whether Jews or Gentiles, whether bond or free.' As therefore in the true Christian community there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith. And therefore if a man refuse to hear the Church let him be considered - so the Lord commands - as a heathen and a publican. It follows that those who are divided in faith or government cannot be living in the unity of such a Body, nor can they be living the life of its one Divine Spirit."
In the eyes of the Roman Catholic Church, which is the one, true Church, there are only the following categories of people:
i.e., those who are members of the Roman Catholic Church;
that is, validly baptized people who have left the Church because they adhere publicly to false teachings and/or non-Catholic sects;
that is, validly baptized people who have left the Church because they refuse to recognize the primacy of the Roman Pontiff, or belong to sects which profess the same;
those who have been ejected from the Church by declaratory sentence of excommunication;
that is, the unbaptized, who fall into two subcategories: (a) Jews,
whose error of resistance to the true Messias has a special name, that of perfidy,
and (b) heathens,
i.e. pagans, idolaters, and people who have no religion at all.
There is no such thing as a "partial communion" between the Roman Catholic Church and non-Catholic sects. To assert that there is a partial communion between the Roman Catholic Church and non-Catholic sects is overtly heretical, since it is directly contrary to the Church's teaching:
Pope Pius IX:
"None [of these religious societies differing among themselves and separated from the Catholic Church], not even taken as a whole, constitutes in any way
and are not that one, Catholic Church founded and made by Our Lord and which He wished to create. Further, one cannot say in any way
that these societies are either members
of that same Church, because they are visibly separated from Catholic Unity."
Pope Leo XIII:
"Jesus Christ never conceived of nor instituted a Church formed of many communities which were brought together by certain general traits - but which would be distinct one from another
and not bound together among themselves by ties which make the Church one and indivisible - since we clearly profess in the Creed of our Faith: " 'I believe in one...Church.'”
Pope Pius XI:
"It is absurd and ridiculous
to say that the Mystical Body can be formed out of separated and disjunct members."
Pope Pius XI:
"It is to depart from divine truth to imagine a Church which one can neither see nor touch, which would be nothing more than spiritual in which numerous Christian communities
would be united by an invisible bond,
even though they are divided in faith."
It is important to understand this Vatican II ecclesiological heresy (Church heresy), for it is the basis of its heresy concerning religious liberty. Critiques of Vatican II tend to center on the religious liberty heresy, but it is merely an outflow of the ecclesiological heresy, which is more grave as it is more fundamental.
St. Augustine said:
“We believe in the Holy Church which is indeed Catholic. For the heretics and schismatics also call their congregations Churches. But the heretics violate the faith by thinking falsely, and the schismatics break away from fraternal charity by their wicked dissensions, although they believe what we believe. For this reason neither the heretics belong to the Catholic Church, which loves God, nor the schismatics, because the Church loves her neighbor.”