I would view this question as a particular application of the problem of evil. Christian disunity is an evil and we should not deny that, but it is an evil which God has chosen to permit for some good reason.
Any comparison to first century Judaism is bound to fail if we look too closely, because the situation was so different from our own. The Pharisees, Sadducees, and Essenes all had aspects of the truth but also suffered from serious errors.
The Pharisees had an almost-correct pre-Christian theology (at least from what we see in the Bible; the writings of Josephus suggest they may have had more contamination from pagan philosophies than we usually assume). However some of their interpretations were wrong and they failed to sufficiently distinguish man-made “fences” from the actual law of God. Also of course were often hypocritically prideful.
The Essenes had an intense and almost monastic spirituality and a communal love reminiscent of that of the early Church. However they had the schismatic policy of rejecting the Temple, plus some bizarre customs and a possibly excessive association of God with the sun.
The Sadducees, though probably the most morally repugnant and doctrinally darkened of the lot, were legitimately skeptical of some of the Pharisees notions, rightly (for that time) emphasized Temple worship, and were not as guilty of pridefully excessive social isolation from the Gentiles and “sinners” as were the Pharisees and Essenes. Also they had a certain claim to historical continuity with Judaism’s past (including most of the Hasmonian kings) which gave at least a credible appearance of legitimacy.
Probably Christianity’s continuity with Judaism can best be connected not to any of these groups but to the average poor Jew in the street or the field, who belonged to none of the schools though his beliefs were most influenced by the Pharisees.
Christianity did not need to unite these schools because it transcended them. It formed a community as close-knit and spiritual as that of the Essenes, with a doctrinal authority and historical legitimacy far beyond that of the Pharisees or Sadducees. The Church itself was founded by God in a way analogous only to that of the Israelite nation as a whole (obviously transcending even that), rather than any of the schools or sects that later arose within Judaism.
With regard to Christian unity, this is something for which we should all earnestly hope and pray. Such a unity of course should not be at the expense of legitimate traditions of other apostolic Churches. But we should not give in to temptations to indifferentism. Christ instituted one Church, and it is to this that all people are in some sense called. We may (now that I see you, ConstantineTG, have joined the Orthodox Church as I thought you might) disagree on which Church visible in the modern world is that one Church founded by Christ, but let us not give up our honest search for truth and our fidelity to whatever we honestly believe Christ’s Church to be.