From Mormon belief statement:
How God teaches men
In order to declare the gospel of Christ, God has called inspired men, called prophets, to teach the world. These men receive a personal witness of the Savior and are given authority to teach his gospel. This authority is called "priesthood." The Bible contains the words of prophets who lived long ago and taught about the Savior. As the prophets teach and testify, the Holy Ghost touches the hearts of people and brings feelings of peace. This is why we feel the spirit (the Holy Ghost) when we study the Bible today. This spiritual confirmation of truth is how God confirms that the message of the prophets is true.
Throughout history God has followed this pattern of revelation to inspired men, who then teach the world, with confirmation of their words through the Holy Ghost. Sadly, people do not always accept the message of the prophets. When the people reject the prophets, this is called "apostasy," coming from a Greek word that signifies rebellion or falling away. When we read the scriptures, we can see a history of God calling a prophet who teaches the people to repent and turn to the Lord. The people eventually turn away from the Lord and reject the prophet, and thus a period of apostasy follows.
Fortunately, God is merciful and patient, and each time that the people reject the Lord, He waits and prepares His people, and, when the time is right, He sends His messengers again to declare His words and restore His gospel.
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.