Antithesis and Common Grace

How can regenerate believers work together with unregenerate unbelievers? If there is an absolute antithesis between the principles of the regenerate and the principles of the unregenerate, how can there be any interaction? Moreover, does God's common grace restrain the unrighteous suppression of truth in the unbeliever? Perhaps Cornelius Van Til can help shed light on this: 

"Because of God’s common grace, this ethical antithesis to God on the part of the sinner is restrained, and thereby the creative forces of man receive the opportunity of constructive effort. In this world the sinner does many “good” things. He is honest. He helps to alleviate the sufferings of his fellow men. He “keeps” the moral law. Therefore the antithesis besides being ethical rather than metaphysical is limited in a second way. It is one of principle, not one of full expression. If the natural man fully expressed himself as he is in terms of the principle of ethical hostility to God that dwells within his soul, he would then be a veritable devil. Obviously he is often nothing of the sort. He is not at all as “bad as he may be.” (An Introduction to Systematic Theology, 45)

 "And common grace is the means by which God keeps man from expressing the principle of hostility to its full extent, thus enabling man to do the “relatively good.” (Common Grace and the Gospel, 200)

"Thus it comes to pass that they of whom Scripture says that their minds are darkened can yet discover much truth. But this discovery of truth on their part is effected in spite of the fact that in principle they are wholly evil. Their discovery of truth is adventitious so far as their own principle is concerned. They are not partly evil, they are not just sick; they are wholly evil, they are spiritually dead. But in spite of being dead in sins, they can, because of God’s common grace, discover truth. The universe is what the Scripture says it is, and man is what the Scripture says he is. On both of these points it says the opposite of what fallen man says. Fallen man knows truth and does “morally good” things in spite of the fact that in principle he is set against God." (A Christian Theory of Knowledge, 44)

"The idea of common grace may not become the basis for a 'neutral territory' between believer and unbeliever... [I]n this world of sin no Christian individual and no Christian organization can be positive and constructive till after they have been negative and destructive.... At this point I may interject that when I thus emphasize the absolute antithesis I am not denying or even for a moment forgetting the doctrine of common grace. That doctrine does not militate against but here as elsewhere confirms the doctrine of the absolute antithesis. Common grace does not overlook ultimate differences. Nor does it when correctly understood, in any way tone down those ultimate differences. On the contrary, common grace helps to point out that things which look alike are not ultimately alike. Common grace points specifically to the fact that similarities between the people of God and the people of this world are but proximate similarities and that these proximate similarities play before the background of ultimate differences." (Essays on Christian Education, 91, 187, 189)

For Pastor Zac's favorite book on these matters, see:

Living in God's Two Kingdoms: A Biblical Vision for Christianity and Culture by David VanDrunen 

For Pastor Brandon's favorite book in these matters, see: 

The Lordship of Christ: Serving Our Savior All of the Time, in All of Life, with All of Our Heart by Vern Poythress