I'll see what I can find for you, Nerd, about the synagogue.

You are framing all of your assertions about Jews and Iraq, as well as other parts of the Middle East, from the perspective of a "post-establishment of the State of Israel" world. In order to understand the perspective of the Mizrahim, you need to see the Middle East through their eyes, which is to say, "pre-establishment of the State of Israel" (I believe this is well before the days of Saddam). I think it's a big mistake to underestimate the effect that the Nakba and the activities of Zionists in the countries of the Middle East had on the way Jews are perceived there.

From what I've been reading from Arabic Jews, it appears that many of them think of themselves as being just as much Arabic as Jewish. They are saying that prior to the time when the Zionists showed up in their communities, they had a good life. They were an integral part of the fabric of the society in which they lived, and had been for hundreds of years. They say that these circumstances didn't change until the Zionists showed up and started promoting their agenda among the people of the region.

Now, as far as Europe is concerned, there is no doubt that Jews suffered quite a lot of discrimination there over the centuries. I think that's pretty undisputed. So maybe it's not so surprising that Europeans were so quick to turn on them during the Nazi period. This does not prove a thing about how the Jews of the Middle East were perceived by the other peoples of the region. In order to say that what the Europeans thought about Jews also applies to what Middle Easterners thought about Jews, it is nessary to believe that all people who are not Jewish are the same. This is a fallacy.

And the fact that the Mizrahim feel that the European Jews practice a form of racism against them (Ashkenazi anti-Semitic tendencies is a term used in one of the articles I linked to) suggests that anti-Semitic discrimination is more of a European vs/Arab problem than the world against the Jews problem, or at least it was back in the late 1940s.