I've got my "simple theory" for at least the leftist overlords -- totalitarians like other totalitarians. Our left LOVED the USSR, they still like Cuba, China has gotten a little too commercial for them but still better loved than say England or certainly Israel.
The linked article tries out a couple other theories ... "relativism" is an all-purpose for both sides of the relationship. While the left holds to "absolute, lock them up if they disagree" relative to white christians supporting gay "marriage", relativism allows them to decide that such rules can be suspended for Muslims -- sure, they might have to avert their eyes a bit when gays are actually thrown from high places or stoned in Muslim countries, but hey -- it allows one to REALLY earn their multicultural diversity chops!
Remember, far left is ABSOLUTE rule of the State, and the State is human, not divine, so "cognitive dissonance" is required. The key skill is to be able to parrot what the party line says in the face of even massive shedding of blood. Six thousand young black men killed in the streets yearly by other young black men need to be completely ignored while marching for "Black Lives Matter" over a couple trumped up justified police shootings of blacks.
From the Muslim side, there are only two political parties -- the D's may support gays, women's rights, sex, drugs, and rock-n-roll, but they support it for INFIDELS! One doesn't have to be a very smart Muslim to realize that if enough Muslims can be brought in, enough kids can be had, enough dead or imaginary votes created, it would be EASY to be Muslim nation -- probably already close to having a "Muslim seat" on the SCOTUS, make common cause with the black seat and who knows?
Besides, they sure are not going to vote with heavily Christian, Jewish-loving, strong US loving and flag waving Republicans! Sure it takes a LITTLE cognitive dissonance for them to vote D, but get real!
The other theory offered is the old liberal "we are really nice to our pets" theory.
I think the issue is more that they see Muslims as a new potential mascot group that they can champion and therefore obtain that cheap sense of moral superiority that comes with riding in like a white knight. I think a lot of liberal attitudes towards minorities aren’t actually based on the good of the minorities, but how good it makes the liberals feel to champion them.It seems completely insane to see folks that would lock someone up for not baking a cake for a gay "wedding" falling all over themselves to defend a group whose religions teachings generally make the Westboro Baptist Church look like really easy going liberals by comparison. After all, Westboro has yet to stone, throw from a cliff, behead, drown or even rape anyone! Let alone threaten to implement laws to make such the standard for behavior!
But then, these are completely insane times.
The real situation here is exactly the same as the discussion of wealth and poverty. Poverty needs no explanation, it is the natural state! It is wealth that has to be created by systems and actions that are successful. The state of nature is poverty.
Evil is the the natural state of a fallen world, it needs no explanation. Is it REALLY hard at all for any remotely intelligent person that still has some contact with what was once the standards of Western Civilization to look at Saudi Arabia, Libya, Egypt, Syria, Iran, Afghanistan, etc, and not see evil? The rape and child molestation of women and young boys, the abject poverty, the repression, the violent attacks on Christians, destruction of cultural/religious icons, stoning gays, etc?
The claim of "liberals" is that the fallen world is not fallen -- but rather that it is GOOD! Their alignment with Islam is actually consistent because ultimately, the destruction of Western Civilization will bring us to a state of nominalist control by POWER. Might is right is morally arbitrary! -- any claim to what many see as "natural" (Biblical) morality is removed. "Morality" becomes whatever POWER says it is -- Islamic "morality" is no better or worse than any arbitrary morality since POWER literally IS "morality" when evil reigns.
"Liberals" love Islam because it is rule by POWER. The natural state of man is always "like likes like".