Prove it! You are doing EXACTLY as I predicted: negating what the verse says because it doesn't fit your pre-conceived view. Let's look at the verses I put forth again:
6 For [God] will render to every man according to his works: 7 to those who by patience in well-doing seek for glory and honor and immortality, he will give eternal life; 8 but for those who are factious and do not obey the truth, but obey wickedness, there will be wrath and fury. Rom 2:6-8
The contrast set up between verses 7 and 8 is one between obedience and disobedience. Those who are obedient through "well-doing" are rewarded with "eternal life." But those who are factious and disobedient will be meted a different justice accordingly.
Paul through the Holy Spirit says that what God will "render" (reward) is applicable to "every man." "Every man" means everyone -- that includes believers. And to further show this point, the Greek that here translates as "render" is the verb apodidōmi. And apodidōmi elsewhere is clearly used as regards believers:
"Henceforth there is laid up for me the crown of righteousness, which the Lord, the righteous judge, will award [apodidomi] to me on that Day, and not only to me but also to all who have loved his appearing. 2 Tim. 4:8
So, contrary to your assertion, Paul in Rom 2 is addressing believers ("every man"). And Paul says that as to "every man" God will render (reward) according to works; to those that are obedient he will give "eternal life" (salvation).
Romans 8:1 There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit. 2 For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.
Romans 6:14 For sin shall no longer be your master, because you are not under the law, but under grace.
Romans 11:6 And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work.
Get set free from that works based fear.