As I previously mentioned, suicide bombers think they can take a short to heaven at the expense of killing innocent people. It is ultimately a selfish act which goes against any moral conscience.
No, it goes against your (and my) moral conscience, but that's because they accept different moral precepts upon which to found their morality.
For them, obedience of Allah, and his will as illuminated by one interpretation of Mohammed, is the paramount concern, though there will likely be cultural influences as well.
For you, broadly, obedience to God, and his will as illuminated by the Orthodox interpretation of the Old and New Testaments is your paramount concern, again with cultural influences.
For me, broadly, adherence to individual freedom and personal liberty are the primary concerns, with other cultural influences as well.
They aren't 'immoral', it's merely that their morality is different - and worse, in my opinion - than yours and mine.
O.