Luke was very careful to report the incident involving Paul and Barnabas in Acts 15:36-41 as simply a historical matter. Paul, Silas, Barnabas and Mark were all ministering in Antioch together. Paul felt compelled to visit all of the places where he had preached the gospel and desired Barnabas to travel with him. Barnabas may have answered “Yes” in haste, but soon it became evident through a ministry conflict that the foursome would divide in two and go in different directions. If we read only what is written we do not see any sin in the account. The fact that it is recorded that Paul and Silas were commended by the brethren does not mean that Barnabas and Mark were not commended, or that the brethren were choosing sides in the issue. Both of the missionary journeys were successful.
I conclude that both Paul and Barnabas were in God’s plan and that He used Paul’s reticence to have Mark accompany him again as a means of directing the parties in separate directions. Paul felt that Mark had proven unreliable in the past (cf. Acts 13:13) and did not have the same faith in his maturity as did his cousin Barnabas, who was probably more willing to take a chance on a member of the family (cf. Col. 4:10).
One can have a very heated discussion with opposing views and not sin. The word used in Acts 15:39 is “sharp disagreement,” and is also used in Heb. 10:24 as “encouragement” or “stir up” in love. Even if the more negative connotation of the word, “irritation” is meant—or even if one or the other party harbored sinful anger (and we are not told that they did)—that does not negate God’s using the division as a means to branch out the missionary effort for the sake of the Gospel. The good news is that Paul later ministered with Mark (2 Tim. 4:11).
Your sensitivity to the effect of such disagreements on the Church is well placed. Paul shares the same sensitivity in Eph. 4:25-27—“Therefore, laying aside falsehood, speak truth, each one of you, with his neighbor, for we are members of one another. Be angry, and yet do not sin; do not let the sun go down on your anger, and do not give the devil an opportunity.” We are each specially gifted as well as hard-wired with a unique personality. Such diversity is critical to the church (as are the various gifts of the Spirit) and should allow each of us the freedom to go in different equally moral directions, as Paul/Silas and Barnabas/Mark did, while maintaining our unity without bitterness. In doing so, we submit ourselves as servants to one another rather than lording it over others by pretending to know precisely what God’s plan for their life entails (Matt. 20:25-27; John 21:20-23).
I appreciated you relating the Romans 12:1-2 admonition to “renew your mind” with the issue of Paul and Barnabas. The critical point of Paul’s words in this passage are not focused on either “transforming” or “renewing.” He focuses on a far more important point: “that you may prove what the will of God is, that which is good and acceptable and perfect.” It isn’t about me. It is about God. It is about each of us being positively involved in furthering God’s perfect will. The transforming and renewing of our minds will occur as we obey.
Paul addressed the “new man” which we have become, so that sin no longer has an ultimate hold on us. We are free to be sanctified. “Knowing this, that our old self was crucified with Him, that our body of sin might be done away with, that we should no longer be slaves to sin” (Rom. 6:6), I am able to be transformed in any way. As actions come from thoughts, this transformation must begin with renewing my mind—which is free to desire and then act in accord with what is good. “Do you not know that when you present yourselves to someone as slaves for obedience, you are slaves of the one whom you obey, either of sin resulting in death, or of obedience resulting in righteousness?” (Rom 12:16).