Repentance is not forsaking sin that you may turn to Christ. It is turning to Christ that you might forsake sin.
When we trust in Jesus Christ we do not simply go to a generic Jesus, but to Jesus Christ, the Savior from sin (Matt 1:21). You do not merely believe in Jesus' existence to be saved (James 2:19) but you trust in him to redeem you from the guilt and tyranny of sin. So when you initially go to him in faith, that us what you are trusting in him for.
The command to repent and believe does not assume the moral ability to do so. For this to happen, the Holy Spirit must show us the misery of our sin and create in our heart the desire to be free from it (Ezek 36:26, John 6:63, 65) Then initial repentance is, seeing we cannot save ourselves from sin, we turn to Christ to rescue us from it. That turning to Christ could be called initial repentance because you no longer want to be under the tyranny of sin, but since you cannot break the shackles of sin yourself you still need Christ, so the actual forsaking of sin only occurs when Christ has broken its bondage and liberated us from its tyranny.
So if people are taught they must first clean themselves up BEFORE Christ will accept them, you have no small doctrinal error.
Calvin said,
"Forgiveness of sins can never come to anyone without repentance, because only those afflicted and wounded by the awareness of sins can sincerely invoke God's mercy... But at the same time that repentance is not the cause of forgiveness of sins....the sinner does not dwell upon his own compunction or tears, but fixes both eyes upon the Lord's mercy alone." -John Calvin 3.4.3
No repentance unless God grants it in Christ (2 Tim 2:25-26)