These days it seems as if many couples, including Christians, do not give their marriages a chance and their marriages end quickly because they are not willing to give up their stubborn ways. My husband and I have been married a long time and went through a lot of struggles, especially our first year of marriage because we, of course, were trying to learn to be a husband and wife, but I would never have thought of putting him away. That being said, if a Christian puts away her husband or his wife for any reason other than adultery, but remains single, is it right for them to be able to teach Bible class, lead singing, etc.? And what about the one who is put away? If they remain single should they be able to continue to teach, lead singing, etc?
You are correct that too few people consider the seriousness of marriage and the commitment it requires. When we look at the past, we find that divorcees used to be less than 1% of the population [Ana Swanson, "144 years of marriage and divorce in the United States, in one chart"].
To divorce and then marry again when the reason for the divorce was not fornication on the part of the spouse is a form of adultery (Matthew 19:9). However, there are times when a Christian might find his marriage ended despite his attempt to hold it together. For example, in I Corinthians 7:12-15 Paul discusses the situation where a Christian is married to a non-believer. It might end up that the unbeliever abandons his marriage. This doesn't give the Christian a right to marry again, but it is also does not imply that the Christian has sinned. The general rule is: "But to the married I give instructions, not I, but the Lord, that the wife should not leave her husband (but if she does leave, she must remain unmarried, or else be reconciled to her husband), and that the husband should not divorce his wife" (I Corinthians 7:10-11). There should not be a divorce, but in the case that one does occur, the Christian is to remain unmarried until reconciliation can take place, if it ever does. Because God provides for this situation, while it is not ideal, it cannot be labeled sinful either.
A mistake many make is to read Matthew 19:9 as if it is saying that the only acceptable reason for divorce is fornication. "And I say to you, whoever divorces his wife, except for immorality, and marries another woman commits adultery" (Matthew 19:9). Two conditions have to be met for adultery to take place -- that is what the word "and" does this in this statement. A person who divorces and remarries commits adultery. The exception is a person who divorces because of fornication and remarries. But notice what is not covered: a person who divorces and does not remarry. For that we have to look at what Paul told stated in I Corinthians 7:10-11. What is is interesting is that Paul says the rule he gives is directly derived from what the Lord has said.
Because I don't know the background or reasons why any person is divorced, I cannot sit in judgment and say that they cannot serve as a Christian if they are remaining unmarried. For all I know, they are obeying the command of God in a bad situation.