So how is this great enemy of faith and propellent of unbelief combatted?

One verse in the Proverbs makes it abundantly clear—Prov. 29:25 The fear of man brings a snare, But he who trusts in the Lord will be exalted. A snare is a trap, which prevents one from obeying the Lord.  Notice also that the contrast states that trusting God is the remedy for fearing or trusting in man.  What people can give to us must be counted as nothing in comparison to the benefits of trusting in God.                       

The same rings true for what people can do to us—Ps. 56:3 When I am afraid, I will put my trust in You. 4 In God, whose word I praise, In God I have put my trust; I shall not be afraid. What can mere man do to me?  And just as fearing and trusting man are close parallels, so are fearing and trusting God—Matt. 10:28 Do not fear those who kill the body but are unable to kill the soul; but rather fear Him who is able to destroy both soul and body in hell.  While battling fear of man, we must realize there are far greater consequences for failing to fear God.                        

Finally, we must check our ruling motive against 2 Cor. 5:9 Therefore we also have as our ambition, whether at home or absent, to be pleasing to Him. 10 For we must all appear before the judgment seat of Christ, so that each one may be recompensed for his deeds in the body, according to what he has done, whether good or bad.   This corresponds to what Jesus said earlier in John 12:26 If anyone serves Me, he must follow Me; and where I am, there My servant will be also; if anyone serves Me, the Father will honor him.  Is that the highest achievement you can possibly fathom or is the esteem from people just as valuable or even more so?  The true answer to that is revealed by the overall disposition of your life expressed in words and actions.