To answer your question, I would say that mere disagreement with the prophet on a particular issue is not the same as apostasy.
You have to keep in mind that we do not believe our leaders to be infallible. Nor do we take every word from the President of the Church to be revelation from God. As Joseph Smith once said, a prophet is a prophet only when he is acting as such.
Even when we disagree with them, we are expected to support and pray for our leaders and to recognize their authority to act in the Church. To do otherwise would be apostasy.
For example, I know latter-day saints who are committed Democrats and quite far to the Left of the political spectrum (at least for Mormons). They disagreed strongly with Ezra Taft Benson's conservative political views. Nevertheless, when he became President of the Church, they supported him wholeheartedly. They were able to separate the office from the man.
"I am here to give this people, called Latter-day Saints, counsel to direct them in the path of life...If there is any elder here, or any member of the Church of Jesus Christ of Latter-day Saints, who can bring up the first idea, the first sentence that I have delivered to the people as counsel that is wrong, I really wish they would do it; but they cannot do it, for the simple reason that I have never given counsel that is wrong; this is the reason" (Journal of Discourses 16:161).
Do you agree that Brigham Young has never given counsel that is wrong?
"I know just as well what to teach this people and just what to say to them and what to do in order to bring them into the celestial kingdom, as I know the road to my office. It is just as plain and easy. The Lord is in our midst. He teaches the people continually. I have never yet preached a sermon and sent it out to the children of men, that they may not call Scripture. Let me have the privilege of correcting a sermon, and it is as good Scripture as they deserve" (Journal of Discourses 13:95).
Do you agree with Brigham Young that everyone of his sermons was Scripture?
"You have heard me say, a great many times, that there is not that man or woman in this Church, and there never was and never will be, who turn up their noses at the counsel that is given them from the First Presidency, but who, unless they repent of and refrain from such conduct will eventually go out of the Church and go to hell, every one of them" (Journal of Discourses 17:159).
Will Mormons go to hell for turning up their noses at the First Presidency's counsel on polygamy, and so forth?
"Some would have us believe that God is present everywhere. It is not so" (Journal of Discourses 6:345).
"Now hear it, O inhabitants of the earth, Jew and Gentile, Saint and sinner! When our father Adam came into the garden of Eden, he came into it with a celestial body, and brought Eve, one of his wives, with him. He helped to make and organize this world. He is MICHAEL, the Archangel, the ANCIENT OF DAYS! about whom holy men have written and spoken—HE is our FATHER and our GOD, and the only God with whom WE have to do" (Journal of Discourses 1:50).
Do you agree with Brigham Young that Adam is God and that he had sex with Mary to conceive Jesus and that this belief of Young's is Scripture?
"How much unbelief exists in the minds of the Latter-day Saints in regard to one particular doctrine which is revealed to them, and which God revealed to me – namely that Adam is our father and God" (Deseret News, 6/18/1873, p.308).
Regarding Christian churches
We ask where Christ's Church is. My conclusive answer is, if the Latter-day Saints do not constitute the Kingdom of God on the earth, the Church of Jesus Christ, it is no where to be found upon it" (Journal of Discourses 2:179).
"Will all the people be damned who are not Latter-day Saints? Yes, and a great many of them, except they repent speedily. I will say further, that many of the Latter-day Saints, except they learn their lessons better, will be judged in the same way. That is my candid opinion" (Journal of Discourses 1:339).
Do you agree with Brigham Young that all people outside of the Mormon Church will be damned?
"The Christian world, so-called, are heathens as to their knowledge of the salvation of God" (Journal of Discourses 8:171).
"Should you ask why we differ from other Christians, as they are called, it is simply because they are not Christians as the New Testament defines Christianity" (Journal of Discourses 10:230).
"There are only two churches on the earth—only two parties. God leads the one, the devil the other" (Journal of Discourses 18:215).
How come you don't agree with Brigham Young on this issue? Is it not Scripture (remember...Young stated that he was never wrong!)?
"We declare it to all the inhabitants of the earth from the valleys in the tops of these mountains that we are the Church of Jesus Christ of Latter-day Saints—not a church but the church—and we have the doctrine of life and salvation for all the honest-in-heart in all the world. Who else has got it? Is it to be found in the creeds of Christendom? It is not" (Journal of Discourses, 12:173).
"The Christian world, I discovered, was like the captain and crew of a vessel on the ocean without a compass, and tossed to and fro whithersoever the wind listed to blow them. When the light came to me, I saw that all the so-called Christian world was grovelling in darkness" (Journal of Discourses 5:73).
"Now I would ask the Christian world a question, and in doing so I do not mean to reflect upon, or cast an insinuation in the least derogatory to, all Christians, or to any who believe in God; but I would ask them, what do you know of God? Take all the divines on the face of the earth and place them in this stand, and beyond the attributes of God they know nothing of Him; they are entirely ignorant of His person. There is the difference between the various religious sects of the Christian world and the Latter-day Saints" (Journal of Discourses 13:144).
Regarding the Jews
"Can you make a Christian of a Jew? I tell you, nay. If a Jew comes into this Church, and honestly professes to be a Saint, a follower of Christ, and if the blood of Judah is in his veins, he will apostatize. He may have been born and bred a Jew, have the face of a Jew, speak the language of the Jews, and have attended to all the ceremonies of the Jewish religion, and have openly professed to be a Jew all his days; but I will tell you a secret—there is not a particle of the blood of Judaism in him, if he has become a true Christian, a Saint of God; for if there is, he will most assuredly leave the Church of Christ, or that blood will be purged out of his veins" (Journal of Discourses 2:142
Ouch...Do you agree with Brigham Young on this? Was he wrong on the Jews?