Read carefully. It applies to those who seek to be justified by the law. How many people who seek to be justified by the law are saved?
Romans 8:12
So then, brethren, we are under obligation, not to the flesh, to live according to the flesh for if you are living according to
the flesh, you must die; but
if by the Spirit you are putting to death the deeds of the body, you will live.
Although the general context is the law throughout Romans 2 to Romans 11.
You will notice that living "in the Spirit" is a common theme in Paul's teaching overall.
Romans 12:9-13
Let love be without hypocrisy. Abhor what is evil; cling to what is good. Be devoted to one another in brotherly love;
give preference to one another in honor; not lagging behind in diligence,
fervent in spirit, serving the Lord; rejoicing
in hope, persevering in tribulation, devoted to prayer, contributing to the needs of the practicing hospitality.
When we see "flesh" and "Spirit" we automatically extrapolate.
Living in the flesh is not solely living under the law to be justified, saved.
Here is an example of the deeds of the flesh.
Galatians 5:19-21
Now the deeds of the flesh are evident, which are: immorality, impurity, sensuality, idolatry, sorcery, enmities, strife, jealousy, outbursts of anger, disputes, dissensions, factions, envying, drunkenness, carousing, and things like these, of which I forewarn you, just as I have forewarned you,
that those who practice such things will not inherit the kingdom of God.
You will not find many of the ten commandments in the deeds of the flesh.
As a general rule we are called to be led by the Holy Spirit and bear the fruit of the Holy Spirit.
Nothing can separate those that call on the name of the Lord and bear the fruit, from the love of God.