In Luke 15:4 Jesus says..."What man among you, if he has a hundred sheep and has lost one of them, does not leave the other ninety-nine in the open pasture and go after the one that is lost, until he finds it?"
The definition of "compromise" is to come to agreement by mutual concession. In theory this sounds like a fundamentally good thing, however most disputes or disagreements arise because of a difference in beliefs. The definition of "belief" is to have a conviction of the truth of some statement or the reality of some being or phenomenon especially when based on examination of evidence. Generally, when there is a disagreement, the two (or more) sides hold different beliefs about the nature of the thing or idea in question.
Compromise is only truly possible when both sides have a lightly held conviction about their beliefs. If two people are looking at a ball and are in disagreement with its color, they can only truly compromise, that is agree on its actual color, if both sides are color blind or are both looking at a black and white photograph of the ball. In this case, neither of them can, with certainty of evidence, lay claim to the “truth” of the actual color. However, if either side is not color blind or sees a color picture of a red ball, they can hardly compromise with the other side’s declaration that the ball is blue. Now, they may be willing to say that the actual color of the ball is of little consequence to them, and to therefore let the other person hold their position, but they cannot, intellectually, change their mind and believe that the ball is now blue.
While the above example is rather trivial, it is reasonable to expect that the ability to compromise becomes increasingly difficult as the importance of the issue in dispute becomes greater and as the strength of conviction or belief intensifies. Compromise is much more difficult when we discuss welfare, abortion, marriage, war, crime, justice, and a whole range of other issues in dispute.
It is also irrelevant which side of the issue you are on. If you have strong convictions about the truth of a position on an issue, then it would be an act of intellectual unfaithfulness to compromise with someone else who holds a differing position.
Another factor in this discussion is the degree to which there is agreement or lack of agreement on whether there is such a thing as “truth”. Christians often find themselves being accused of being unwilling to compromise to a greater degree than others. I believe the primary reason for this is the fact that Christians, who hold to a Biblical world view and who believe the Bible to be God’s word to man, have a standard of truth which cannot be changed. The current culture says increasingly that truth is relative and evolving. This results in numerous situations where Christians have a clear, unchanging standard of truth behind their beliefs and the culture around them does not. This is always going to leave Christians being unwilling (or unable) to compromise.