there are times when the Holy Spirit protects the Church from error. We believe it just doesn’t err in these situations. However, did the Holy Spirit allow the Christian church to split apart in several instances?
No. People have freedom to follow or not follow the inspirations of the Holy Spirit. and the Church is One and will never split apart - those in schism and heresy are to some extent separated from the Church, something we define as “not being in full communion”.
I wonder if the theological separations of Christianity somehow bring Christ to people who otherwise might not embrace it?
No. Christ said to the Father: “I want them to be one flock with one shepherd”. Christ cannot contradict Himself. And what you call “theological separation” is the simple removal of truths from Sacred Tradition along with the insertion of errors (which in the past we used to call “heresies”). As for people going to Christ through others rather than through His Holy Church, that is not a sound argument, because, as Christ said, “if they believed in Moses, they’d believe in Him”. Anyone reading the Scriptures would believe in Christ and enter His Church. To believe in Christ and not enter the Church is to believe also to the deceptions, errors, and lies grouped into the doctrines that were born outside of the Church, confusing man-made teachings with divine revelation. The Church, in fact, is the mystical Body of Christ, and one cannot truly “bring Christ to people” unless that means bringing them to full communion with the Church and bringing the Holy Eucharist to them.
Those who can’t accept a dual nature of christ, or Papal infallibity, for example, might be turned off by Christianity if they had no other option.
That’s truly their own problem. Remember John 1? “He was in the world, and though the world was made through him, the world did not recognize him. He came to that which was his own, but his own did not receive him.” And also: “those who listen to you, listen to me; those who reject you, reject me.” (Lk 10:16)
Is this an “economia” of the Holy Spirit? I’ve always thought that God doesn’t really worry too much if you think the real presence comes from “transubstantiation” or some other polysyllabic method.
There’s no problem in avoiding the limitations of human language, as long as we don’t go around saying: “it’s just bread” or “it’s symbolic”, and we discern the Body and Blood of Christ, that is, the Real Presence. In the past, in very ancient times, the Church referred to this great miracle as “transmutation”. Later, because of the rampaging heresy against the Holy Eucharist, the Church better defined what exactly was that changed, and went to the term “transubstantiation”, to clarify that the substance is what changes. But to call it anything else as to dismiss the fact that in the Holy Eucharist is present the living Christ, in Body, Blood, Soul, and Divinity is indeed to greatly upset the Lord, who spoke through the Apostle: “anyone who eats and drinks without discerning the body eats and drinks judgment on himself.”
It also seems to me that if the Holy Spirit protects us from error on things like the immaculate Conception, he wouldn’t make a mistake by letting the churches split if it was not the will of God.
God does not “let” or “not let”, He just “lets”. It’s what we define as “free will”. God “let” Lucifer rebel and drag with himself a big part of the heavenly hosts. That does not mean this was God’s will.