Do not repay anyone evil for evil. Be careful to do what is right in the eyes of everyone. If it is possible, as far as it depends on you, live at peace with everyone.
Any passage of Scripture has to be considered in its context. The directive to do right in the eyes of everyone is in the context living in the midst of tensions in relationships, perhaps at work, at home, or elsewhere. How do we navigate such?
We do what we can and leave the rest to God. God will take care of any wrong that needs to be made right, aside from any wrong we might need to make right, along the way.
There is a certain basic aspect of being a Christian, of following Christ in which we can’t worry about what the world thinks. We try to be true to Christ, to the gospel, to righteousness and justice as God prescribes, regardless.
At the same time, we must be sure that we’re not causing any offense of our own that will make it harder for people to see the light of Christ. We must not cover that light with our own darkness. Paul expresses this idea perhaps more directly here, again to be considered in its own context, but still appropriate for this problem in general:
Do not cause anyone to stumble, whether Jews, Greeks or the church of God— even as I try to please everyone in every way. For I am not seeking my own good but the good of many, so that they may be saved. Follow my example, as I follow the example of Christ.
This should be our passion, something close to our heart. As we seek to follow Christ and his light for ourselves, and in doing so, be a light to others.