Anticipate conflicts before they happen
We should expect conflicts to occur (2 Tim 3:12) and try to anticipate them ahead of time. We should ideally think through the issues involved biblically well ahead of time, so we know exactly where we stand and why. Some conflicts arise completely out of the blue, and in these we need simply to trust God that he will give us the words to say (Lk 21:14-15). If we are unsure it is best to err on the side of caution (Rom 14:23) saying that we are unhappy and would like to give the matter more thought.
Try to defuse conflicts before they arise
We should look for some way to be able to defuse conflicts before they arise - as Daniel did so masterfully early on in his career (Dan 1:8-16). Daniel and his colleagues were faced with a royal directive which if obeyed would have led to them eating food that God's law did not allow them to eat. Daniel anticipated the problem, approached the next man up the authority chain and managed to suggest an alternative solution (a vegetable diet) that enabled he and his colleagues to remain faithful to God without causing difficulty or embarrassment to others involved. His move ultimately led to the whole court seeing the wisdom of God's law and brought reform in the system.
Ask why the conflict has arisen
We must be sure that the difficulty has arisen as a result of our being faithful to God rather than being unfaithful (1 Pet 2:19- 20). If we are genuinely at fault ourselves then we need to apologise for our part in the disagreement. This may at times be difficult to discern in the heat of the moment and some time to reflect on the situation perhaps with the advice of some independent Christian we respect may be wise. It does not follow that because we have been accused of wrongdoing, we are necessarily at fault (Rev 12:10).
Be prepared to take the consequences
We need to make our stand and take the consequences. Usually we will find that our fears don't eventuate. Sometimes God may use the circumstances to vindicate us and our stand may result in some positive change in other individuals or in the system. Occasionally we may stand to lose our popularity, reputation, place on a training scheme, job or worse but this is what carrying the cross is all about. Everyone who desires to live a godly life in Christ Jesus will be persecuted (2 Tim 3:12) and we should be prepared to 'take our share of suffering' (1 Tim 2:3).
Look for a compassionate third way
We should always look for some compassionate third way out of the dilemma. Some ethical decisions may seem like choosing between two equally undesirable alternatives: for example between letting a patient die in severe pain or giving them a lethal injection. Referral to a more experienced colleague or transfer to a hospice specialising in pain relief may resolve the problem. Similarly practical support and adoption is a viable third way to the undesirable alternatives of abortion and keeping a child one is unable or unwilling to support.
Jesus was remarkable at discovering the third way no-one had contemplated in so many of his ethical dilemmas, and will help us by his Spirit to do the same. Not rushing into diabolical quick-fix solutions will make us much better researchers in the long run.
So on the one hand we need to resolve to be obedient to what the Lord has commanded, and on the other we need to be searching for compassionate Christian alternatives. This is the way Jesus walked. It is the path of the cross - obedience regardless of the cost (Lk 14:28-33) and a willingness to be part of the solution by bearing the burdens of others ourselves (Gal 6:2).