Well a conservative muslim and a politically conservative American are two very different animals. Not that the mouth breathers watching CNN would understand the distinction.
Conservative as an adjective is entirely appropriate here. As you say, the difference is in what is trying to be conserved.
American conservatives are trying to conserve the ideals of the American Revolution and uphold the Constitution.
Conservatives Muslims want to return to the ideals of the first decades of the Muslim Revolution. To coin a phrase.
The two revolutions have nothing in common and are inherently at war.