Instead of asking this particular question, let's start with some simpler questions.
1. Are there legitimate reasons why someone might choose to disassociate with something like the Boy Scouts or the Girl Scouts or intramural sport team?
Some reasonable reasons might include: getting older, not as interested in the particular activity, leader was a molester, financial misappropriate (e.g., misuse of funds), don't agree with their charter.
2. Are there legitimate reasons why someone might choose to quit being part of a club e.g., a book club, a stamp collecting club, etc.?
Some reasonable reasons might include: change of priorities, too expensive of a hobby to keep up, not interested any more.
3. Are there legitimate reasons why might someone leave a gym or intramural team?
Some reasonable reasons might be: I was injured by an accident somewhere else, I developed tendoinitis, unsafe equipment, chronic pain, financial embezzlement, overcharging for membership, etc.
4. Are there legitimate reasons why someone might choose to leave a place of employment?
Some reasonable reasons might include: moving, want a change of pace, e.g., more or less challenging work, financial misappropriation / fraud, changing careers.
5. Are there legitimate reasons why someone might choose to break off a dating relationship?
Some reasonable reasons might include: serious deal breakers, the other person was unfaithful, the other person is a compulsive liar / compulsive gambler, this person is not trustworthy.
6. Are there legitimate reasons why someone might divorce, even biblical ones?
The main one that everyone agrees upon is adultery. Especially for an unrepentant adulterer. Others would consider in the case of abuse or abandonment.
7. Are there legitimate reasons why someone might choose to not be a member of a non-ICOC or non-ICC church?
Some reasonable reasons might include: the congregation is too far (you and/or the congregation has moved), they are teaching false doctrine, financial misappropriation, misconduct by the leaders (e.g., pedophile priests, sexual scandals).
All of the above questions are to show that it is reasonable to leave any other organization.
8. What would be reasons why you, as a current member, would leave the International Churches of Christ or the International Christian Church?
(please list your reasons using the above)
Would it suffice for:
1Kings 18 comes to mind, and the two people involved are Elijah and Obadiah.
Elijah's name means "The LORD is my God," (El=God, Eli thus is "my God" with the first person common singular pronoun attachment, jah/Yah is the short or personal form of YHWH) a polemic against Baal worship -- King Ahab's and Queen Jezebel's problem. As we read in the chapter before in 1Kings 17, Elijah is called to go eartward and hide in the Cherith/Kerith Ravine, east of the Jordan (River). What's significant about this fact is that Elijah is now outside of Israel (East of the Jordan River) and then Zarephath in the region of Sidon (in Phoenicia, again outside of Israel). Elijah is an "outsider", who is a prophet calling Israel and her king Ahab and queen Jezebel to repentance (returning to God).
Obadiah's name means "Servant of the LORD" (Obad/ebed=servant, iah/yah again the short/personal form of YHWH). He is in contrast a significant person in the employ of King Ahab -- "over the household" (ESV) or "palace administrator" (NIV), and a devout follower, who feared the LORD greatly. He took it upon himself to defy the evil queen and hid a hundred prophets in two caves and fed them with bread and water (18:3-4). So he is an insider who seeks to obey God and reform (change evil practices to godly practices) from "within."
Both are necessary -- and don't lose sight of that. Both have strengths and weaknesses; there are difficulties with both positions. If members choose to stay, they must still remember to strive to reform. It is possible, however, that reform is not possible.
This pattern has been repeated throughout history, especially church history -- for instance, Puritans sought to purify the Church of England from within, where Separatists (or Independents) departed from the Church of England to establish their own churches so that they could follow God in ways they believed would honor Him more biblically. Some of these Separatists formed the Mayflower Company eventually came to America, although Puritan and Separatist churches often looked very similar and in some circumstances merged to form Colonial Congregationalist Churches. Additionally, the Fundamentalist/Modernist Controversy resulting in a number of Princeton professors leaving Princeton Seminary and forming Westminster Theological Seminary is another data point; these two groups were at odds over numerous things from what should the Church be focused on/the task(s) of the Church (i.e., Christian Mission) to doctrines such as the Incarnation and Atonement to Sin. The Fundamentalists eventually separated from the Modernists/Progressives.
Staying put and trying to change/purify/reform from within is important; if everyone who wishes to honor God ends up leaving, it becomes far more difficult to reform. However, all organizations and movements go through phases of progress or growth (even beyond numerical growth), plateau, stagnate, and either decline until they cease to exist or go through a time of renewal. There's a great deal of discernment and wisdom, gifts of the Holy Spirit, to figure out whether a particular stagnating organization or church is headed to its eventual demise or whether it will go through renewal.
Renewal is a work of the Holy Spirit and therefore unpredictable.
I would posit that for those who wish to remain to renew a particular church of movement,
(1) they are committed to this vision, even long-term (like even over multiple decades), as culture is glacial to change from below (if leadership is united/unified and aligned, culture changes over about a decade);
(2) they are able to maintain their core values and membership within the dying church or movement does not cause them to significantly compromise or corrupt their core values;
(3) they maintain "life-lines" -- lines of fellowship and communication outside their churches for prayer, support, encouragement, assistance, even constructive feedback, observation(s), and being reality-checks
I can expand on the first two thoughts (as I think the third is fairly self-explanatory):
(1) Insiders can change culture better than outsiders. And those in power can change it faster than those who aren't. However, leadership has to send frequent aligned messages for culture to change.
(2) Insiders are able to obey God and don't have to do things that would compromise who they are or what they believe. They also have to ask the question, "How much (sin, problem, decay, etc.) is too much?" or "What sacrifices am I willing to make or am I not willing to make to follow the truth?"