The answer depends on what they are angry about.
For many years I was very angry with the church I grew up in. My anger was such that it was keeping me from God. I actually hated Christians. My issue was hypocrisy. My mistake was confusing God with His people. People are almost perfect hypocrites. We talk a much greater game than we play. We all do it from time to time and many of us do it continually.
If we are going to judge God through the lens of His worst followers, then God and His church will not be an alternative for us. This means we miss out on having a relationship with the source of all love and truth. At some point we have to accept that God’s people, although better than they would be without Him, are still people. This means expecting hypocrisy.
It is much like the adjustment we make when we get married. We have an ideal of what our spouse should be based on their persona presented during courtship. After marriage we discover that some of what person was advertising doesn’t match with reality. Now we have a choice to make. We can cling to our ideal of who they should be or we can begin to accept who they really are and work toward a successful marriage. Ditto for life in the church.
Another reason for many people’s anger with the church comes from what the Bible calls “taking offense”. Someone does something hurtful to you and you become offended. You choose not to forgive [because being offended is a form of self-pity and it is very pleasant emotionally] and so that relationship is now tainted. This happens with another person, and then another person, all with the same result. Soon you have more offenders in the room than “friends.” Now it’s time to leave….
The fact is, we should expect to be offended. It is impossible to live with humans without being offended. God knows this and has provided a solution. Forgiveness. Church is a wonderful place for growth in character because it provides us with many offenses to forgive [numerically, even more than marriage.]The third common reason why people leave the church and “miss” God is because someone has had the courage to confront them on something wrong they have done.
Christians are very interesting. They come to God because they have seen themselves clearly and do not like what they see. They want to change and so they come to a place that is in the change business – church. Someone comes along and points out some way that they need to change and they are shocked. How dare she speak like that to me! Who does she think she is?!?! She has all sorts of things wrong with her too!!! I don’t have to take this, I am LEAVING! All this is, is another example of hypocrisy.
We say we want to change but when someone comes along to help us do that, we are offended. We all say we want God to point out our weaknesses but when He uses someone other than Himself to do that, we become angry.
Finally, there is a good reason to be angry at the church but it is rare. There are churches that abuse people. The misuse of spiritual authority occurs BUT it is much rarer than what is usually claimed. Where a church uses guilt and manipulation to control people it is an abusive church and the abused person should leave. The problem is that any of the first three reasons for anger with the church are often claimed to be abuse and they are not. A decision to leave a church is a radical decision with spiritual consequences. It should not be made quickly. Forgiveness is the coin of the realm in the Kingdom of God and we should spend it generously.