In the first place, the Church's unity is one of its notes, so that it is simply not possible for any other condition to exist: "One, holy, catholic and apostolic Church."
In the second place, this unity cannot refer merely to an "invisible church," as Protestants like to think. The Lord Jesus Christ prayed that we would be one for a purpose: "that the world may believe that thou hast sent me" (Jn. 17:21). Now it is impossible for an invisible unity to persuade anyone of anything, precisely because it is unseen. Hence this unity of which the Lord speaks is clearly a visible unity.
In the third place, and for the same reason, this unity simply cannot have to do with interior, subjective beliefs: because once again, this is not a visible thing, and our unity must be something that may be seen. Hence it must be visible and objective.
In the fourth place, the Church does not require Catholics to explicitly and comprehensively believe all the same things. This would be an impossibility anyway: we are not all gifted theologians like St. Augustine or St. Thomas or Pope Benedict. Further, to require this would effectively necessitate the exodus of Catholics from life in the real world for the cloister so that they might spend all their time studying theology. Obviously this is ridiculous, for Christ prays, "I do not pray that thou take them out of the world, but that thou keep them from evil" (Jn. 17:15). Furthermore, not everyone is capable of understanding and explicitly believing all that the Church teaches. Children are not. The mentally handicapped are not. But salvation is not only for capable adults. Since it is not possible for Catholics to explicitly believe all the Church teaches, and in fact it would be ridiculous to have such a requirement, the Church says that an implicit faith is required. The practical upshot is that if we, in our ignorance, hold to some error or other while nevertheless fully and sincerely intending to believe all that the Catholic Church proposes for belief, we do in fact have that implicit faith, and we are in fact one with the Church, and the Church is in fact united just as Catholics say that she is.
Now with respect to the fact that we see Catholics disagree (as we do), we must understand this in any of three ways. A Catholic who believes something contrary to what the Church teaches:
- Is unaware of his error, but would hold to the truth if he knew what it was
- Is unaware of his error, and would not recant it even if he did know what the Church taught
- Is aware of his error, and knows that it is contrary to what the Church teaches, and obstinately refuses to repent
"Catholics" of the second and third sort are really Catholic in name only, for they have formally abandoned the faith. They have functionally excommunicated themselves. They must repent of their obstinate unwillingness to believe what the Church teaches before it's even worth bothering about the specifics of their errors.
I suppose a fourth class might be those who deliberately hold themselves in ignorance of what the Church teaches, pretending on that basis to be free to believe what they wish. This is really as bad as the second group above: it amounts to lying to God and to themselves.
The upshot, apologetically speaking, is this: yes, Catholics have differences of opinion. But they absolutely do not have differences of belief. Why? Because genuine Catholics always intend sincerely and genuinely to believe exactly what the Church teaches, even if in ignorance or through lack of ability they may possibly err in some particular or other. If there are some who pretend to be Catholic who nevertheless deliberately deny what the Church teaches...well, they aren't genuinely Catholic. In one respect, therefore, we might say that it should not be very difficult to identify genuine Catholics from others. We might simply ask, "Do you sincerely intend to believe all that the Catholic Church proposes for belief?"
We can say more. It is ridiculous for Protestants or others to expect 100% unanimity among Catholics on all topics of dispute. The Church does not require our beliefs to be united on literally everything, but rather only with regard to matters of faith and morals. So I suppose we should say that for Protestants to point at differences of opinion on non-essentials among Catholics as a "proof" of Catholic disunity is nothing more than to knock down a straw man. On the contrary, despite the fact that we have liberty with regard to non-essentials, Catholics retain their essential unity.
To be fair we must concede that in their wisdom the bishops and the Pope have not seen fit to formally excommunicate all those who call themselves Catholic but who deny one or more things taught by the Church. I do not know why. I personally would think that for the sake of avoiding scandal that such people ought to be firmly called upon to repent or depart. The fact that they are in our midst has nothing to do with the objective unity enjoyed by Catholics, however.
Lastly, it ought to be said that the same sorts of things simply cannot be said with regard to Protestants. In the first place, they do not agree amongst themselves with regard to identifying the essentials of the faith. In the second place, they do not agree among themselves with regard to the content of those essentials even when they do agree about the particular topics that are supposed to be "essential." In the third place, it is entirely typical for Protestant denominations to be formed over things that even they would not describe as "essential" themselves: as when the Presbyterians split over alcohol consumption in the 40s or 50s of the last century. Hence we see not just Lutherans and Methodists and Presbyterians and Baptists, but Missouri Synod Lutherans and Wisconsin Synod Lutherans and ELCA Lutherans, and United Methodists (an ironic name) and Free Methodists and Wesleyans, and Orthodox Presbyterians and PCAers and PCUSAers, and American Baptists and Southern Baptists, and so forth.
Any honest Protestant will concede their own lack of unity. Some might even be so bold as to claim it as a "feature" rather than a bug. But it is only an grossly uninformed or deliberately disingenuous one who would seriously try to fling a tu quoque at Catholics over unity!