In spite of the confusion it often causes, the noun anti-semite does not mean "one who hates Semites", it means "one who hates Jews". Those Arabs who hate Jews often take advantage of the confusion to claim that they are not anti-semites because they don't hate Jews. To claim that anti-semites hate Arabs is a complete red herring. If you feel compelled to bring it up as a means of solidarity with Arabs, please don't. If you feel compelled to bring it up to show that you are smart, please don't. It only shows you didn't do your homework. There is a much broader definition of anti-semite, it is an adjective which means "Discriminatory especially on the basis of race or religion."
Wilhelm Marr coined the word. The Simon Wiesenthal Center points out that this was an attempt to discrimate on Jews as a race, rather than on Judaism as a religion. I think it is safe to assume he knew what he meant, especially since he founded the League of Anti-Semites. Moshe Zimmerman calls Wilhelm Marr "The Patriarch of Anti-Semitism", and notes that he turned his back on the movement at the end of his life. The Peace Encyclopedia has a FAQ. Here are Dean Esmay's thoughts on the subject.
I recently encountered this red-herring in the comments to this Dean Esmay post, as well as this one. When I commented on the posts I only checked dictionaries, and one of them let me down. Check out the Merriam Webster definition, which only mentions Jews. Dictionary.com is cites three dictionaries. The American Heritage and Wordnet only mention Jews, but the Webster's Revised Unabridged Dictionary says, "Opposition to, or hatred of, Semites, esp. Jews." Here are more dictionary entries, all of which only mention Jews:
The Dictionary of Difficult Words
So the dictionary vote is seven to one in favor of the Jew-Hater definition, plus five other sites which agree. I rest my case.