Many do try to add works to salvation... Yet, the price was paid for us on the cross. Not all obtain the grace offered by Jesus. We are not universalists who believe that all are saved, but we believe that Jesus died on the cross, so that all had opportunity to be saved.
What the Lord made plain in the Word, is that we are to 'repent'. That is not a work, it is an inner change of mind toward sin. Repent is the Greek word 'metanoia' and means to have a change of mind. Our minds while a sinner are led by the lust of the flesh, the lust of the eyes, and the desires of life... but... when we see the offer of salvation, and our hearts are changed to wanting salvation in Jesus, that change of mind allows the grace of God to flow upon us, washing away our sins, cleansing us.
That moment we are saved. We are saved, as the Bible says, 'UNTO GOOD WORKS'. Therefore the good works follow. The reality of our change of mind, the reality of the salvation upon us, is the works that begin to flow from us. 'FAITH WITHOUT WORKS IS DEAD', and if we would go on in our many sins, not even feeling guilty about them, we did not have 'repent', and we did not receive the 'grace'.
One of the first works, after salvation is 'confession of sins'. I John 1:9, 'if we confess our sins, He is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.' This is written to Christians in I John. In John' s day there were some who denied they had sin, would not confess sins, claimed to be sinless, even when sins were shown in their lives. They felt salvation meant they could sin and it not be counted sin. John dealt with that group rather bluntly, and said 'if you say you have no sin, you lie...' That group were not even saved. There was no fruit of the grace they claimed.
Other works follow that confession. The confession of sins allows the Lord then to begin to cleanse away the damage sins did to us before salvation. IT is a process we continue in during our life with Him.
What brought us salvation was the grace of God. It was provided entirely by Jesus on the cross. His resurrection then guaranteed ours. Sins that follow salvation need 'repentance' too, and the confession of our weaknesses keep the salvation cleansing flowing upon us, and we are in a sanctification process. The only sin that removes us from salvation is the rejection of Jesus. If we remain in Him, as weak as we may be at times, we are still saved. Yet, God saves no one who does not want Him, and who would reject Him willfully, and determinately. Barring that stupid decision, we stay saved, and sometimes struggle with the flesh wanting us to change our mind from God back to sin. But we keep that 'repentant' heart, changed from wanting sin, to wanting Jesus, and we stay in His salvation plan.