Does the sinner need to repent in order to be saved? I'm afraid so! Not the best of news to any who want to enjoy Heaven while they can hold unto their sins, but this is how it stands in the Bible, and we fail to preach the whole truth if we either neglect it or (worse still) oppose it.
Repentance in the Bible is a change of mind, induced by faith in the gospel message, but it is a change of mind that will lead to a change of direction. IOW, you can talk all you want about a change of mind, but if it doesn't work its way through to the behaviour, then your words are empty words.
Does this leave us open to the charge that we are preaching salvation by faith plus works? Are we asking the sinner (say the drunkard) to give up his sins in order to be saved? Are we preaching reformation of character as part of the mix that leads to forgiveness of sins? We say, like Paul, at this point not only "In no wise" but "God forbid!" The sinner has no power in himself to forsake his sins in any Evangelical sense of the word. He might be able to swap his sins i.e. cease being a drunkard and become a good living Pharisee, but he cannot forsake them in the manner demanded by the word of God. Furthermore, unless the Spirit of God has being moving upon his heart, the sinner has no desire to forsake them. They are the darling sins of his heart. He loves their darkness rather than the light, for his deeds are evil (John 3:19) Only the goodness of God will lead him to repentance (Romans 2:4) and such must be given unto him (Acts 11:18) While he has a responsibility to forsake his sins - it is never right to stay in sin - yet that same sin has chained him and so he needs nothing less than the mighty power of God's saving truth to set him free (John 8:32-36) Repentance preachers are not looking for reformation of character before salvation. We do not tell (say) drunkards to go away, clean up their lives and come back when they have been off the drink for 3 or 6 months (zero tolerance) and then (and only then) we will explain John 3:16 to them.
A sinner hears the gospel. He learns that there is a hell for sins and a Saviour in Jesus Christ etc. Being convicted of his sin by the power of the Holy Spirit, he expresses his desire to be saved. We ask him: "Saved from what?" We are not looking here for theologically precise answers. He is a sinner from off the street and not necessarily a doctrinaire. We are not going to nitpick his language, but we need to know why he has expressed a desire to be saved. If he just wants to be saved from the hell below, but not from the hell within (i.e. the chains and bondage of sin) then he has not properly understood the gospel. That might (at least partly) be our fault. Have we faithfully preached Christ as the Saviour of His people from their sins? (Matthew 1:21) Did we emphasise in our message that Jesus Christ is the One Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works. (Titus 2:14) If not, then we must make up the slack here as we chat with this interested sinner. We lay it down the line, gently but firmly, that he cannot know peace with God if he is still living in rebellion as a sinner. God does not save His people in their sins, much less for their sins. Is he willing to then forsake these sins that alienate him from God and is he willing to cast the destiny of his soul upon the finished work of Jesus Christ as the only hope of his salvation? He affirms. We do not (as said) send him away for a trial period. There and then, we point him to the Lamb of God in faith. If the Spirit of God has truly being doing His work, that sinner's life will be changed for ever - not by mere outward, man produced reformation, but by the mighty power of the gospel that automatically makes those that be in Christ to be new creatures. There is no more merit in repentance than there is faith. Neither of them earn salvation for the sinner, but both are required to bring him salvation. Christ does not pardon those who are living in brazen rebellion.
This is the old time gospel, as proclaimed by old time Evangelicals, both Calvinists and non Calvinists alike. Listen to John R Rice, whose books sold in the millions: