Hello John146, one of my favorite and most useful commentaries is The KJV Bible Commentary. Here's what it has to say about Romans 8:1 KJV (the highlights in bold are theirs, not mine, while the tildes ~~ are mine, not theirs, just FYI).
There is condemnation to those believers who walk after the flesh and not after the Spirit. The bible speaks of temporal condemnation. Romans 8:1 says, "There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit." Modern Translations leave out the part that says, "who walk not after the flesh, but after the Spirit." The KJV says, as a part of having no condemnation, two things are required: We have to be in Christ Jesus, and walk not after the flesh, but after the Spirit. The enemy wants Christians today to justify sin instead of battling against it. So the enemy will do everything he can to give a person a water down version on His holy Word to promote the idea that there is no condemnation for not following the word of God.
8:1. There is therefore now no condemnation to them which are in Christ Jesus. The word condemnation (Gr katakrima) means ~more~ than just the opposite of justification; it indicates that we are not servants to the penalty for our sin, but that guilt and penalty have been removed at the cross. Therefore, for those who are in Christ Jesus, ~we do not live under the constant threat of judicial punishment by God~. In many ways this chapter is the consummation of Paul’s argument concerning the depravity of man and the righteousness God provided to meet man’s need. The expression, who walk not after the flesh, but after the Spirit is not in the original. There should be an exclamation point after the expression therefore now no condemnation to them which are in Christ Jesus! ~Hindson, E. E., & Kroll, W. M., eds. (1994). KJV Bible Commentary (p. 2238). Thomas Nelson.
The thing is, I wouldn't have a problem with the KJV/NKJV's additional qualifying phrase in v1 (even if it really was in the Autograph), because the context of Romans 8 tells us that "who walk not after the flesh, but after the Spirit" is a description of ~ALL~ who are true believers, ALL who are "in Christ Jesus", as The KJV Bible Commentary also helps make clear for us above (IOW, it is not describing 2 different classes of believers). NONE of us walk after the Spirit perfectly, of course (well, save the One, of course), but when the opposite is true, IOW, when an impenitent person continuously, "walks after the flesh and not the Spirit", THAT is the perfect description of an unbeliever (someone who was ~never~ saved).
If a person who claims to have become a Christian has no desire to delivered from their carnality and worldliness on this side of the grave, IOW, if their sole desire in doing so was to escape God's wrath and the fires of Hell in the age to come, then their "claim" of salvation should be regarded as nothing more than that (as they are CINO).
God bless you!!
p.s. - just for good measure, here's what another well-known commentary (that uses the KJV text exclusively) has to say about Romans 8:1. Once again, the text in bold is theirs, not mine.
1. There is therefore now, &c.—referring to the immediately preceding context [OLSHAUSEN, PHILIPPI, MEYER, ALFORD, &c.]. The subject with which the seventh chapter concludes is still under consideration. The scope of Ro 8:1–4 is to show how “the law of sin and death” is deprived of its power to bring believers again into bondage, and how the holy law of God receives in them the homage of a living obedience [CALVIN, FRASER, PHILIPPI, MEYER, ALFORD, &c.].
no condemnation: to them which are in Christ Jesus—As Christ, who “knew no sin,” was, to all legal effects, “made sin for us,” so are we, who believe in Him, to all legal effects, “made the righteousness of God in Him” (2 Co 5:21); and thus, one with Him in the divine reckoning. There is to such “NO CONDEMNATION.” (Compare Jn 3:18; 5:24; Ro 5:18, 19). But this is no mere legal arrangement: it is a union in life; believers, through the indwelling of Christ’s Spirit in them, having one life with Him, as truly as the head and the members of the same body have one life.
who walk not after the flesh, but after the Spirit—The evidence of manuscripts seems to show that this clause formed no part of the original text of this verse, but that the first part of it was early introduced, and the second later, from Ro 8:4, probably as an explanatory comment, and to make the transition to Ro 8:2 easier. ~Jamieson, R., Fausset, A. R., & Brown, D. (1997). Commentary Critical and Explanatory on the Whole Bible (Vol. 2, p. 239).