The ones who had soiled their garments had "washed their garments in the blood of lamb", but they sinned, thus had "soiled their garments"--"Let us rejoice and be glad and give the glory to Him, for the marriage of the Lamb has come and His bride has made herself ready. It was given to her to clothe herself in fine linen, bright and clean; for the fine linen is the righteous acts of the saints."
Mine says "the righteousness of the saints". That's different. The righteousness of the saints is Christ's righteousness, reckoned unto those whom He has chosen to salvation, and which is manifested through His faith.
Christ's faith was/is imputed to those whom He saves. As a part of His faith also are His righteousness and His works, and therefore, after being imputed to them, from God's viewpoint, it as through Christ's faith, righteousness and works are theirs.
[Rev 19:8 KJV] 8 And to her was granted that she should be arrayed in fine linen, clean and white: for the fine linen
is the righteousness of saints.
[Phl 3:9 KJV] 9 And be found in him, not having mine own righteousness, which is of the law, but that which is
through the faith of Christ, the
righteousness which is of God by faith:
Moreover, Rv 3 says the ones who will walk with white garments with Christ are "worthy" and will not be blotted out of the Book of Life. God, Who does not change, says "the one who has sinned against Me I will blot out of My Book", so we have even more reason to believe "soiled their garments" means "they sin". What is the sin?
To sin regarding eternal judgement is to be under the law of sin and death - or said another way, the law of works. It is at the same time both law AND sin. This should not be confused with God's law or the moral dictates that He gave to man.
The law of sin and death manifests itself in our trust in our works for justification and not in Christ as Saviour. We are born under it, and just by being under it, we sin - it is within the heart of natural man and until saved by Christ, we remain under its power.
Rom 8:2
For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.
To figure that out, you need to know the commandment: "Believe on the Name of God's Son, AND love one another"--so, they were breaking one of those.
But to believe on the Name of God's Son requires the gift of faith resulting from salvation through the fruit of the Holy Spirit. Man is unable to provide this to himself. To love one another likewise is a gift through the Holy Spirit.
[Gal 5:22 KJV] 22 But the
fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness,
faith,
[1Pe 1:22 KJV] 22 Seeing ye have purified your souls in obeying the truth
through the Spirit unto unfeigned love of the brethren, [see that ye] love one another with a pure heart fervently:
As for those who are born of God not continuing in sin, it specifies, "for His seed remains in him"--but Hebrews warns that a man's heart (parable of the sower) can change, saying,
Hebrews 3
12Take care, brethren, that there not be in any one of you an evil, unbelieving heart that falls away from the living God.
13But encourage one another day after day, as long as it is
still called “Today,” so that none of you will be hardened by the deceitfulness of sin.
14For we have become partakers of Christ, if we hold fast the beginning of our assurance firm until the end...
So, if a person rejects the seed (eg, rejects correction), they "go on sinning" and are "worthy of much sorer punishment" (Heb 10).
Sin is to trust in our works for salvation and not in Christ as Saviour. Trust in Christ occurs only if God is working within someone to will and to do of His good pleasure, because natural man simply cannot do so of himself. All Christians, especially those who are new to, or unlearned in the doctrines of Christ and faith, require spiritual instruction, admonition, and exhortations - that is how they/we learn. Nevertheless, God must be working within them to bring the increase forth to fruition. Below we are informed that God used Paul and Apollos for such, but, it was God alone who brought the increase forth. And if He does, it cannot be reversed.
[Phl 2:13 KJV]
13 For it is
God which worketh in you both to will and to do of [his] good pleasure.
[1Co 3:5-7 KJV]
5 Who then is Paul, and who [is] Apollos,
but ministers by whom ye believed, even as the Lord gave to every man?
6 I have planted, Apollos watered;
but God gave the increase.
7 So then
neither is he that planteth any thing, neither he that watereth;
but God that giveth the increase.