(I Corinthians 6:6 [KJV]) But brother goeth to law with brother, and that before the unbelievers.
From the first occurance in 1 cor 6:6 we can see that unbelievers are unbelievers like atheists and agnostics and other people that dont believe in Jesus Christ.
(I Corinthians 14:23 [KJV]) If therefore the whole church be come together into one place, and all speak with tongues, and there come in those that are unlearned, or unbelievers, will they not say that ye are mad?
We see in 1 Cor 14:23 that unbelievers can be in a church where true believers are active.
 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?  And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?  And what agreement hath the temple of God with idols? for ye are the temple of the living God; as God hath said, I will dwell in them, and walk in them; and I will be their God, and they shall be my people.  Wherefore come out from among them, and be ye separate, saith the Lord, and touch not the unclean thing; and I will receive you,  And will be a Father unto you, and ye shall be my sons and daughters, saith the Lord Almighty. (II Corinthians 6:14-18 [KJV])
We should not be unequally yoked with unbelievers . Unbelievers are unrighteous because you can only be justified by faith (Romans 3:20). We should come out from among them .
(Proverbs 9:7 [KJV]) He that reproveth a scorner getteth to himself shame: and he that rebuketh a wicked man getteth himself a blot.
 And when Felix heard these things, having more perfect knowledge of that way, he deferred them, and said, When Lysias the chief captain shall come down, I will know the uttermost of your matter.  And he commanded a centurion to keep Paul, and to let him have liberty, and that he should forbid none of his acquaintance to minister or come unto him.  And after certain days, when Felix came with his wife Drusilla, which was a Jewess, he sent for Paul, and heard him concerning the faith in Christ.  And as he reasoned of righteousness, temperance, and judgment to come, Felix trembled, and answered, Go thy way for this time; when I have a convenient season, I will call for thee.  He hoped also that money should have been given him of Paul, that he might loose him: wherefore he sent for him the oftener, and communed with him.  But after two years Porcius Festus came into Felix’ room: and Felix, willing to shew the Jews a pleasure, left Paul bound. (Acts 24:22-27 [KJV])
We can preach about judgement to come to an unbeliever as we see Paul do to Felix .
And he said unto them, Go ye into all the world, and preach the gospel to every creature. (Mark 16:15 [KJV])
We can preach the gospel to unbelievers.
What should we do to an unbeliever?
We should separate ourselves from them. We should not rebuke them. We could preach the gospel to them and also preach about judgement to come to them.