I have been reading some of your web-based information, and I have a few questions; If a youth pastor in the church of Christ (don't worry, not yours) that has serious secrets in their family such as a gay son who is now out of the house, and a daughter who has had not one but two pregnancies out of wedlock and divorced, would this type of family behavior be considered "all right" for him to continue to be a youth pastor and to continue to lead other families? Also, since each church of Christ is independent, who is responsible for making sure pastors like the one described are living right and held accountable for their actions? Do you have the scripture to back up your responses?
The terminology gets in the way of your question. There are no "youth pastors" in the Bible. The work of spreading the gospel is not divided up by age groups. What most people in denominations call a "pastor" is more closely associated with the term "preacher" in the Bible. For details see: Pastors and Preachers.
By the qualifications of elder or pastor in I Timothy 3 and Titus 1, the man you describe would not be qualified for the position. An elder must have "faithful children not accused of dissipation or insubordination" (Titus 1:6). The congregation would not accept such a man as an elder. If an elder strays from doing what it right, it is the preacher's duty to rebuke him. "Do not receive an accusation against an elder except from two or three witnesses. Those who are sinning rebuke in the presence of all, that the rest also may fear" (I Timothy 5:19-20).
Whether such a man could preach at a congregation would depend on whether he changed since he raised his children. I suspect that you are describing an ongoing problem that this man is not addressing properly. The congregations I know of would reject such a man because he is unable to set a good example of Christian living. "Let no one despise your youth, but be an example to the believers in word, in conduct, in love, in spirit, in faith, in purity" (I Timothy 4:12). A man cannot teach the gospel while not living it. If a preacher develops a problem, it is the elders of the congregation who would take the initiative to get the preacher back on track. But even without elders, each member has a duty to help those who fall into sin (Galatians 6:1-2).
Thank you for your response.