Is it normal to get depressed because there are people in the world who hate God, and even more so because those who claim to be Christians have thought processes that are not much different than those out in the world?
"Brethren, join in following my example, and observe those who walk according to the pattern you have in us. For many walk, of whom I often told you, and now tell you even weeping, that they are enemies of the cross of Christ, whose end is destruction, whose god is their appetite, and whose glory is in their shame, who set their minds on earthly things" (Philippians 3:17-19).
It is sad to consider the fate of those who focus on the things of this world, whether never knowing Christ or those who have turned their backs on Christ. However, depression implies an extended state of sadness and such doesn't match Paul's attitude shown throughout the book of Philippians. "Rejoice in the Lord always. Again I will say, rejoice!" (Philippians 4:4). While there are sad things in the world, a Christian's overall outlook is one of joy.
To the lost, we can teach. "Therefore we also have as our ambition, whether at home or absent, to be pleasing to Him. For we must all appear before the judgment seat of Christ, so that each one may be recompensed for his deeds in the body, according to what he has done, whether good or bad. Therefore, knowing the fear of the Lord, we persuade men, but we are made manifest to God; and I hope that we are made manifest also in your consciences" (II Corinthians 5:9-11). Yet, we must remember that each person has his own free choice. We won't be able to persuade everyone. In fact, relatively few will make it to heaven. "Enter by the narrow gate; for wide is the gate and broad is the way that leads to destruction, and there are many who go in by it. Because narrow is the gate and difficult is the way which leads to life, and there are few who find it" (Matthew 7:13-14).
Rather than focus on what we cannot control, we focus on where we are going while doing what we can. "Brethren, I do not regard myself as having laid hold of it yet; but one thing I do: forgetting what lies behind and reaching forward to what lies ahead, I press on toward the goal for the prize of the upward call of God in Christ Jesus" (Philippians 3:13-14).