"Is that not true for Muslims? Or do they not fight because they just don't care?"
They do not fight because they do not have a desire to stand up for and defend this country. They do not love and cherish this country. They will not go to war against fellow Mooselimbs.
To fight this is one of Bush's strategies - to eventually tip the Muslim frame of mind to the point where they begin to doubt. When enough of them start believing "Allah is not with them [the terrorists]," it will be the beginning of their end.