Most Islamic ideologies do not do that. Jihadist movements are exceptions to this. During the Crusades, Christians did not reject that behavior – their philosophy was “Kill them all [i.e. even if they were Christians] and let God sort it out”. Do a search for “Caedite eos. Novit enim Dominus qui sunt eius.” sometime for more information on that.

Such history, including a few regrettable incidents in history of the LDS church really ought to remind us not to get too far from the scriptures, the Holy Spirit, and the prophet.

As to why Jihadists do what they do, the answer is probably different for each group but has something to do with trying to correct an apostasy. Some also appear more politically than religiously motivated.