Left-leaning new sites absolutely refuse to take a stance against Islamic terrorism because it doesn't fit in their worldview
I disagree. As far as I can tell, left-leaning people hate terrorism. The difference is that some people believe that "most current terrorists are Muslim" means the same thing as "most current Muslims are terrorists", and some see that those statements are different.
I hate terrorism. I'm not fond of Islam, but then I'm not fond of Christianity either. Both want to control how I live and who I can marry. But I don't blame Islam for terrorism; I blame terrorists for terrorism. Which do you blame?
Note that I blame Christian bigots for the (now being dismantled) anti-gay movement, but I don't blame Christianity or all Christians for it; I blame bigots. And if people thought that they could still get away with KKK-style lynchings in the US, I suspect that we would see more Christian terrorism. Fortunately, the governments which turned a blind eye to that practice in the 1900s have gotten better. I hope that the governments in the middle east will also improve over time.