C'mon, this is kinda silly.
While it's certainly true that Arabs are semites, the term "anti-semite" was coined in 1879 by a German Jew-hater named Wilhelm Harrih, as a scientific name for his philosophy concerning Jews.
Sure, he was a wacko, but that's the doofus etymological origin of the word and its parlance to this day. Trying to redefine it now is not only pointless, but doesn't clarify anything.
We can stipulate from time to time that Arabs and Jews are both of Semitic stock, and if you want to call someone "anti-Arab" or "anti-Moslem," just use those terms.
You can use them against me if you like, since I agree with Sabra more than I disagree.
However, you may want to note that I've called no one on this thread an anti-semite.