There are a few ways to explain it. The first is the silliest, that Jews have a history of being persecuted, and that therefore, they have a knee-jerk reaction to the persecution of any group, Muslims or whatever. But that doesn't really hold water, because when a country prohibits the immigration of a class of people, it's hardly persecuting them. But if you do accept that immigration restriction is persecution, then just about every country on Earht is persecuting some category or categories of people. Look up immigration laws of any country you like and you'll find that to be the case.
So, the same organizations that want no immigration restrictions in US law, Jewish and otherwise, should logically be raising hell about the immigration restrictions of countries other than the United States and Europe, most of which are much more stringent. And, dare I say it, the immigration laws of Israel, which, basically, say that Jews can immigrate but nobody else can — and yes, there are exceptions to that, but can you imagine the reaction that would result if the US had a law that said only Christians could immigrate?
So, no, it's not the knee-jerk anti-persecution thing.
Is it because, as some have said, that Jews have a special affinity for Muslims and like being around them? If so, that would be a small minority of really crazy Jews, because Muslims certainly don't have a special affinity for Jews. Yes, I know that they do, in theory, have an affinity for "people of the book" [link]. And that classification definitely includes Jews and Christians. But that's the theory, and the practice is that Muslims are especially hostile towards Jews for a number of reasons. So, no, that can't explain it.
And that exhausts the theories of why Jews in general, and all Jewish organizations that I've heard of, are so much in favor of Muslim immigration into the West, to include the US and Europe. Well, except for one theory, and I'll leave it up to you whether it should be taken seriously or not. This is really two theories. The first is that the Jewish people, or at least the overwhelming majority of Jewish leaders, just plain hate Western Civilization and the Christianity that underpins it, and tend to favor anything that will break it down or destroy it. That includes all forms of decadent behavior, from the drug culture to sexual deviance, and most certainly includes cheering on immigration of nonWestern people into the West, the more hostile they are to the West and its values the better. And who is more likely to be hostile to all things Western than Muslims in general? And the second theory is the same as the first, except that the promotion of such immigration and decadence isn't designed to destroy the West, but to weaken it and transform its population to a hodgepodge of people with no intrinsic unity of purpose. Obama said it explicitly:
“Over the long term, I’m pretty optimistic, and the reason is because this country just becomes more and more of a hodgepodge of folks,” [link]
So I'll leave these last two theories up to you to judge. I know they seem very crazy and unlikely, but any other theories that might explain the phenomenon involve lizard people and flying saucers. I hope this post illuminates the issue for you.
Quibcag: The crazy girl with the sign is Sensei from Denkigai no Hon'ya-san (デンキ街の本屋さん?, lit. "The Electric Town's Bookstore").