Probably the hardest thing for wingnuts to understand is that, for Muslims, the words “Islam,” “Islamic,” and even “jihad” are positive words. When you call something Islamic, the presumption is that it is something good. There’s a reason that radical political/terrorist groups tend to call themselves things like “Party of Allah,” “Islamic Jihad,” or the “Muslim Brotherhood.” It’s not to scare the Texas congressional delegation. It’s because those names arouse sympathy from ordinary Muslims.
A Brit might not like the sound of the “Daughters of the American Revolution,” but they aren’t named that to scare Brits. They’re named that because they’re proud to associate themselves with the American Revolution, and they know most Americans will respect the name if not necessarily the specifics of their agenda.
So, going around denouncing “Islamic” terrorism is really a horrible way of driving a wedge between terrorists and everyday Muslims. Everyday Muslims will never agree that being Islamic is suspect or somehow bad.