You claim that we [you and I] aren't in unity, and you seem to base this claim on the fact that we differ over certain Catholic doctrines. I certainly hope that unity doesn't require that I believe exactly like everyone else. I think we can't be in [religious] unity if we don’t believe that faith in the blood of Christ cleanses us from sin; that Jesus is the Son of God; that He was born of a virgin; that He rose again and is interceding at the right hand of the Father; and that the Bible was inspired by the Holy Spirit to guide us in our daily lives so that we might be more like Him. There probably are a few additional beliefs that would be helpful to hold in common if we expect to have unity within the church. And you undoubtedly share these core beliefs. But I don't see why we need anything beyond agreement regarding those core beliefs in order to have Christian unity.
This position is quite common, I think, especially among the Evangelical communities. It amounts to what we might call "mere Christianity". According to "mere Christianity", what is important are certain essential or core doctrines, and we need to agree on those essential doctrines. All other teachings or practices are matters about which we may disagree, without thereby having caused a schism or divided the Church.
There is a certain sense in which Catholics agree with "mere Christianity". There are points of doctrine about which the Catholic Church has made no determination. (Think of the debate between the Dominicans and the Jesuits in the sixteenth century regarding the nature of divine grace, for example.) On such points Catholics may disagree, without that disagreement being either schismatic or heretical, or diminishing our unity. And so in that sense, the Catholic Church grants that we don't all have to "believe exactly like everyone else" in the Church in order to be in full communion, i.e. in full unity with each other. And yet when a candidate or catechumen is received into the Catholic Church, he says the following sentence: "I believe and profess all that the Holy Catholic Church believes, teaches, and proclaims to be revealed by God." For a Catholic, therefore, "all that the Holy Catholic Church believes, teaches, and proclaims to be revealed by God" is essential to the faith, not optional.
So what are the problems with the "mere Christianity" position? Fr. Dwight Longenecker has addressed these in his book More Christianity. Here I want only briefly to address a few. For the first fifteen hundred years after Christ, if you had asked any Christian what are the fundamentals of the faith, he would have pointed to the Creed and the sacraments. But we find the sacraments only in the Church; and the Creed itself presents as an 'essential' of the faith that we believe in the "One, Holy, Catholic and Apostolic Church." In other words, from the point of the early Christians, there is no "mere Christianity" that sets aside the Church, or treats the Church as irrelevant or superfluous or non-essential to the Christian faith. That explains the early dictum of the fathers that "he cannot have God for his Father who does not have the Church for his Mother". So that historical fact should give pause to any contemporary advocating some kind of Church-transcending "mere Christianity".
Second, the idea of finding a lowest-common doctrinal denominator between all the various factions and schisms, and treating that lowest-common doctrinal denominator as the "essentials of the faith" ultimately leaves us with no doctrinal content for the "essentials of the faith", for in that case there is no ground for a principled distinction between schisms and heresies. (That is because insofar as "mere Christianity" says anything about "the Church", it treats the Church as an invisible entity, i.e. as merely the plurality of all genuine believers of the content of those "essentials of the faith". For the problem with that notion see my posts here and here.) Church-transcending "mere Christianity" is for that very reason strapped with an authority vacuum that does not provide a ground for distinguishing between schisms and heresies. For example, in "mere Christianity", apart from the authority of the Church, there is no ground for an authoritative determination that Arianism is a heresy. There is just one's own interpretation of Scripture versus that of the Arian. (And don't think that heretics didn't appeal to Scripture: see here and here.) And so to find a lowest-common denominator between oneself and the Arian means that something even like "Jesus is God" must be left out of the "essentials of the faith". In this way, the "mere Christianity" position provides no authoritative determination of what exactly are those "essentials of the faith". By default, then, each man decides for himself what are the essentials of the faith. And thus for "mere Christianity" what is described as "the essentials of the faith" is a chimera, an abstraction treated theoretically as though it were a concrete particular which we all can self-evidently recognize. But the "essentials of the faith" are not self-evident. Protestants often disagree regarding which doctrines are true, let alone regarding which doctrines are essential. That is precisely why there are so many factions within Protestantism. In short, when each man decides for himself what are "the essential doctrines of the faith", the result is not unity, but disunity, because there is then no authoritative determination and delineation of what those essential doctrines of the faith are. Without the authority of the Church, "mere Christianity" is merely a feel-good fiction.
"Mere Christianity" moreover leaves no ground for an authoritative determination of how much unity Christ wants Christians to have. The person defending the "mere Christianity" position has no way of knowing whether he has exchanged the sublime and sacramental unity Christ wants His people to have for a cheap substitute involving agreement on a few propositions. For the same reason he has no way of knowing whether his proposed unity is too strong, and that perhaps merely holding hands and singing Kumbayah with all the members of the World Council of Churches is the unity Christ wants. Thus the same problem that faces the "mere Christianity" position regarding determining "the essentials of the faith" also applies to its notion of how much unity Christ wants Christians to have. In this way, the "mere Christianity" position is self-refuting, for it arbitrarily sets up a standard of unity (i.e. agreement on some indeterminate set of doctrinal propositions) that closes itself off to a broader "mere Christianity" involving a different form of unity (e.g. liturgical, practical, social). For this reason, "mere Christianity" necessarily collapses into individualism, for that is what it is in essence, precisely because of its [implicit] rejection of the Church and the Church's authority.
Pope Benedict XV (the previous pope Benedict) said, "Such is the nature of Catholicism that it does not admit of more or less, but must be held as a whole or as a whole rejected". About forty years ago, J.B. Phillips wrote a book titled Your God is Too Small. Those persons advocating some form of "mere Christianity" need to see that their proposed Christian unity is likewise "too small". It falls short by orders of magnitude from the sacramental and ecclesial unity Christ calls us to in John 17 and St. Paul calls us to in 1 Corinthians 1:10. The 'unity' of "mere Christianity" is indistinguishable from utter fragmentation and disunity. For a helpful article on the subject of "mere Christianity" from a Catholic point of view, see Kenneth Whitehead's article titled 'Is there a "Mere Christianity"?'.