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.
"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)
Secondly, given that repentance is a grace (2 Tim 2:25-26) and all grace is found in Christ (Eph 1:3), those who are still in the bonds of corruption are morally impotent to clean themselves up or forsake sin BEFORE coming to Him. That would be to usurp the office of Christ
It is for this very reason we need to come to Him in the first place, that He might sanctify us, break the bonds of sin and liberate us from captivity so that, in Christ, we might forsake sin and put sin to death by the Spirit.
As the Spirit renews us and reveals the misery of our sin, we flee to Christ to rescue us from both its guilt and power. Only He can forgive our sin (justification), and only He can set us free from its bonds (sanctification). Forsaking sin only begins after we are joined to Christ, who breaks its power over us.
The way I see it there are three main theological positions regarding repentance:
1) The belief that we come to Christ to be delivered from the guilt of sin, but NOT ITS POWER. To want Jesus to deliver from hell, but not from sin. Here obedience is considered optional for a later stage of discipleship. (This is the antinomian position, often referred to as the carnal Christian doctrine)
2) The belief that we must first forsake sin in order to come to Christ. (the neonomian position)
3) That we sinners have no hope in ourselves so, by the regenerating grace God, we turn from sin to Christ, the Savior, to deliver us from it... BOTH its guilt AND power. (The biblical, confessional position)
So far we have established that only those who want to be saved from their sin go to the Savior to be redeemed from it, correct? They want to be liberated from being under its tyranny, or they would never turn to Jesus, right?
So you could demonstrate that this initial part of repentance (fleeing to Christ to be liberated from sin) comes BEFORE faith and must accompany justifying faith, but it is important in the ordo salutis (order of salvation) to put repentance AFTER faith, since that is when it is consummated. We certainly do not forsake sin before coming to Christ. And since no complete repentance, or forsaking of sin, can take place apart from trusting Jesus, it logically must come after faith.
It is the trusting in Jesus alone to rescue us from the guilt and power of sin which justifies us. We do not rest on our repentance for the pardon of sin, but we certainly cannot be pardoned without it. Repentance (the forsaking of sin) is really the fruit of sanctification, not justification, so it is not legal or forensic like justification is. But we must remember that sanctification is also a component of salvation. And if we do not want to forsake sin, it is a sure sign that we did not come to him for salvation from it.
It is important to remember that it is not what we do that technically saves us, but Christ. Our faith (by itself) is not what saves us but faith in the Redeemer. And not even our faith but the grace of God in Jesus Christ is that what saves us. Faith and repentance both spring from the Spirit bringing us into union with Christ.... they are the fruit of the redemptive work of Christ but do not contribute to it. Both come from the Spirit renewing our hearts in Christ.
The Westminster Confession 15 defines repentance as follows:
I. Repentance unto life is an evangelical grace, the doctrine whereof is to be preached by every minister of the Gospel, as well as that of faith in Christ.
II. By it, a sinner, out of the sight and sense not only of the danger, but also of the filthiness and odiousness of his sins, as contrary to the holy nature, and righteous law of God; and upon the apprehension of His mercy in Christ to such as are penitent, so grieves for, and hates his sins, as to turn from them all unto God, purposing and endeavouring to walk with Him in all the ways of His commandments.
III. Although repentance is not to be rested in, as any satisfaction for sin, or any cause of the pardon thereof, which is the act of God's free grace in Christ, yet it is of such necessity to all sinners, that none may expect pardon without it.
IV. As there is no sin so small, but it deserves damnation; so there is no sin so great, that it can bring damnation upon those who truly repent.
V. Men ought not to content themselves with a general repentance, but it is every man's duty to endeavor to repent of his particular sins, particularly.
VI. As every man is bound to make private confession of his sins to God, praying for the pardon thereof; upon which, and the forsaking of them, he shall find mercy; so he that scandelizeth his brother, or the Church of Christ, ought to be willing, by a private or public confession and sorrow for his sin, to declare his repentance to those that are offended;who are thereu
Repentance and Salvation by Patrick Ramsey
Justifying Faith by Patrick Ramsey
Faith and Repentance by Dr. Sinclair B. Ferguson
What Came First: Repentance or Forgiveness? (MP3) Carl Trueman, Todd Pruitt
Repentance: No Pardon Without It, by Chad Van Dixhoorn
Ordo Salutis (The Order of Salvation) @Monergism