I come from a marketing background so I try and figure out what these liberals think to support a religious minority that hates their liberal left values worse than the most racist KKK neonazi skin head.
I can think of these three things that create a cognitive dissonance on Islamists (emphasis on the Islamists) and the liberal left mind:
1) Because the right wing may have a point on Islamists the left needs to defend Islamists as a racial and minority thing. They somehow view it as a slippery slope - if people dislike Islamists then they will somehow become racists against other minorities.
2) Islamists are exotic primitive minorities - it's like the liberal white persons dream to go help primitives in the jungle or some such. In their fantasy mind helping Islamists will someday civilize them and show that the liberals farts don't stink.
3) They view them in militant anti-western terms - Islamists are oppressed like the Vietnamese commies were so that plays into their militant anti-American fantasies.
In reality, if we made Catholic women wear religious clothing like a hijab the feminists would be in an uproar - but if Muslims are forced to dress that way - it's their choice and your are a closed minded Christian if you say otherwise. It is a liberal metal disorder - they embrace Islamists to give the middle finger against Christian conservatives to show how inclusive the liberals are as a propaganda tool. It is the best explanation I can come up with for why the left is embracing the most anti-liberal religion on the planet.