The war is *NOT* against Islam. The war is against a pack of criminals, who merely use Islam as a rallying cry. Nobody (sane) is preaching genocide against the Islamic world.
In any event, there is no prohibition agains fighting during Ramadan (but only the misguided, misunderstood fanatics, of course.)If they want sensitivity, they should probably get out of the jihad business, or risk getting shot in the stomach during fasting hours.

my .02,
Hugh