No, its not because they like what they're doing. Some do, many more than liberals would like to admit. But even the vast majority of them, these silent supporters, are irrelevant. The Muslim world is not democratic or well organized. The levers of power are available only to a small few like the Gulf monarchs or military dictators like Assad and Sisi. So most Muslims aren't doing anything because they're poor and politically disenfranchised and a minority of the Muslim world, like the Sunni monarchs of the Gulf, see ISIS and its kind(Al Qaeda, Al Nusra etc) as useful pawns.
And btw the people who are fighting ISIS are Muslims. The Shiite militias in Iraq and Hezbollah from Lebanon are two of the most effective forces against them and Assad has various sects fighting under him(in fact I remember reading that his military has one of the highest ranking Christian of any of the regional Muslim majority countries) and of course Iran is behind all of them. And the Kurds are mostly Sunni Muslims.
