Not all christians - the catholic church teaches that it is never moral to commit a sin for the greater good.
See the catechism of the catholic church # 1756 and 1789:
One may never do evil so that good may result from it. (See
http://www.vatican.va/archive/ccc_css/archive/catechism/p3s1c1a6.htm#1789 . This line of thinking is also used in the explanation of why contraception may not even be used for good reasons, as the church sees it as intrinsically immoral. The same goes for abortion, although I think it becomes a grey area when it comes to ending ectopic pregnancies.)
We had a thread about this recently in OBOB, the question was: is it allowed (or 'moral') to lie in order to save a life? (Lying is seen as always immoral according to the catechism.) So, may you choose a lesser evil in order to avoid a greater evil? Concrete situation: (the old story) you have jews hiding in your attic, the nazis come at your door and ask you whether you have jews in the house. If you say no, you lie. If you say yes, the jews will die.
According to catholic morality, you still should not lie - although most catholics did not agree with it; they would lie (well, that's always an assumption, but at least they thought they would lie in that situation) because indeed, it doesn't seem moral to let people die just because you didn't want to lie. The lie is trivial compared to people's lives.
That doesn't mean that the catholic church would not forgive people who choose to do the lesser evil to avoid the greater one - but officially I think they would need to repent and confess the lesser evil. And, well, I don't equate the catholic church with God. Even if the church does not forgive the lesser sin that is committed to prevent a greater one (if the only option to prevent the greater evil was to do the lesser evil), I, like you, believe that God would.