Saying that Christians are always righteous and always sinful may seem like a contradiction, but it is not. Positionally Christians are always righteous but practically they are always sinful.
Christians are always righteous because they have the righteousness of Christ credited to them. This righteousness is received by faith alone in Christ alone. Jesus takes the sins of believers on himself and gives them his perfect righteousness. The Christian is able to stand before God justified because of the righteousness of Christ.
But at the same time Christians are still sinful in this life. They still struggle with sin. A Christian is bothered by his sin and lives a life of repentance. They still do things they should not do and do not do things they should. Christians do become less sinful but they also become more aware of their sin.
We must point out that Christians do not continue on the same old way. A true Christian has been born again or regenerated. The Christian is a new creation, old things have pasted away (2 Corinthians 5:17). If there is no difference in one claiming to be a Christian, then that person is most likely not a true Christian. A Christian is characterized by a desire to honor and obey God.
But all the practical righteousness of the Christian does not measure up to God's perfect standard. Even when doing right things often the motivation is not truly righteous. No one truly keeps the law of God. Only in heaven will Christians be without sin. But no one deserves to go to heaven. We are only saved by God's grace alone, by faith alone, because of Christ alone.
Always Righteous
Philippians 3:9
2 Corinthians 5:21
Romans 1:17
Romans 3:22
Always Sinful
Romans 7:14-25
1 John 1:8-10
1 John 2:1-2