Incompatible moral values
Clash of moralities
Conflict of interest
Situations in which there are moral reasons in favour of two or more incompatible actions, especially where it is a difficult matter of individual judgement to decide between them.
The sharpest and most obvious cases occur in war, but they are present in a lesser degree throughout life if only because time and resources devoted to furthering one end have to be taken from time and resources devoted to furthering another.