when they should be called anti-Jewish?
A real anti-Semite would hate Arabs as well as Jews.
From Merriam-Webster online.
To address the OP:
[shrug].
The fact that it is common usage is not a reason for it to be common usage.
Bobby Fisher, the chess player, made this same distinction once. Based on previous statements he had made, a reporter asked him if he was an anti-Semite. Fisher replied that Arabs are Semites and he didn’t hate Arabs, so he wasn’t an anti-Semite. Not exactly the strongest denial of prejudice ever made, but then again Fisher’s a loony.
Anyway, to address the OP, there has been a long-standing debate (which has appeared on this board among other places) about whether Jews are members of a religion or an ethnic group. People who support the former position might conceivably argue that anti-Jewism could only be directed against practicing Jews while anti-Semitism can be directed against anyone of Jewish ancestry even if they’ve never been inside a synagogue. Being as intolerance against Jews is usually directed on an ethnic basis, the common term is therefore more apropriate.
As for the fact that Arabs are Semites also, when the term anti-Semitism was first coined in Western Europe, the number of Arabs in Europe was virtually non-existent in comparison to the number of Jews, so the overlap probably didn’t seem significant.
This subject has been covered ad nauseum in the past. Asking this question is like asking, “Why do we call it a microscope? I mean, ‘micro’ in Greek just means small, so a microscope should see all small things, not just things that are so small they can’t be seen with the naked eye.” Total sophistry. The word “anti-Semite” means “anti-Jewish”; that is its usage, and despite the fact that its root might refer to a more general classification, the word means “anti-Jewish”, period.
And also debated on these boards - the difference between anti-Jewish/anti-Semitic and anti-Israeli.