@Andiamo, the beauty of God's Word is that it is so intricately constructed that nothing can alter what God intends to convey when you read the Word as a whole rather than pick out a verse here or a verse there. I think there's little doubt that the clause "who walk not after the flesh, but after the Spirit" was not in Paul's original at that point, but was indeed a logical part of the idea he writes 3 sentences later. And if you like, I can tell you exactly why. But for now, to continue my point that God protects His Word, what does walking after the spirit and not after the flesh mean?
At its most basic level it means that our life is given us by the Spirit and not by the natural world, and therefore the focus of our lives is on spiritual things not only on natural things. So, in essence, having that insertion of "who walk not according to the flesh, but the according to the Spirit" does not change the meaning of God's Word in Romans 8:1.
You see, that clause is introduced by the grand truth ”therefore, there is no condemnation for those who are in Christ Jesus" and is immediately followed by "for in Christ Jesus the law of the Spirit of life set you free from the law of sin and death." The form of the Greek verb "set you free" describes a one and done deal. The law of the Spirit of life (faith in Jesus Christ and His finished work which, as Scripture plainly reveals, gives you eternal life) has freed us from the law of sin and death (striving in your own ability to please God which, as Scripture equally plainly reveals, leads to eternal death.) When viewed bracketed by those two statements, the relative clause "who walk not after the flesh, but after the Spirit" conveys Biblical truth: namely, that there is no longer any kind of condemnnation for us because our lives, being IN Christ Jesus, are now in the realm of the Spirit not In the realm of the flesh and, therefore being now governed by the law of the Spirit of life, we are now no longer governed by the law of sin and death.
So, the insertion of the clause we have been discussing into the end of verse 1 does not change the meaning of God's Word, when we properly divide it. The problem comes when it is improperly divided and people understand it to add a condition to our not being condemned: specifically that in order not to be condemned we must walk --behave, live-- our lives in a certain way ... in other words, if we interpret that inserted phrase to mean that our salvation depends not exclusively on Christ's work but on our behavior, then WE have altered God's Word. But, of course, there are many, many other verses in the Bible that make it clear that we're saved by faith alone in Christ alone.
This is what I mean when I say that God's Word is so cleverly constructed that taken as a whole it prevents misunderstanding or mistranslation. We see a good example of that in the Jehovah's Witnesses
New World Translation where they have purposefully mistranslated a number of passages so that their bible will support their false doctrine. But in doing so they have actually introduced contradictions into their bible, contradictions that require them to continually retranslate and change in an attempt to eliminate them. But the second you begin to change God's word it will never fit together, you're faced with a hopeless task of altering it to fit your beliefs.
But understanding that God's Word cannot be harmed by any copyist's mistake or intentional insertion, does not mean that we should just ignore them and allow such things to exist despite the weight of the manuscript evidence. My problem with allowing that relative clause to exist at the end of verse 1 is that, placed in that location, it not only interfer with the flow of Paul's thought that he is communicating --in Christ there is no condemnation because we are now governed by the law of the spirit of life in Christ Jesus and no longer the spirit of law and death-- but it also introduces an occasion for Satan to muddy the waters of salvation by raising the idea that our freedom from condemnation by God is somehow connected to the way we live. Do you see how that clause does that at the end of verse 1? Now it is no longer a simple statement that there's no longer any condemnation for those who in Christ Jesus but instead it conveys the idea that there's no longer any condemnation for those who are in Christ Jesus
and who walk not after the flesh. Now, that that interpretation is incorrect can be discovered by reading the rest of the epistles in the New Testament, but unfortunately too many teachers who teach legalism use it to insert the false idea that somehow what we do is more important than (or even as important as) what Jesus did.
Nevertheless, despite the possible misinterpretations that the change I have discussed can raise, whether that relative clause is tacked onto the end of verse 1 or left in its proper place in verse 3, it does not change God's Word. And certainly not if we apply proper Berean study of the Word in its entirety. Therefore, dear sister, do not let it worry you. I can assure you that there is no place in the Bible that in 50 years I have come across where a copyist's change, or some disagreement in manuscript, has altered the meaning of God's Word to us. We can trust it 100%.
If you would like a longer discussion of this I can help with that, but in the meantime, I hope this helps.