Many times I've heard argument whether you spell it antisemitism or anti-Semitism.
If you look at the Wikipedia pages about Antisemitism it also mentions the spelling with the dash.
As far as I understand the point is that anti-Semitism would somehow indicated that it is against "Semite" despite the commonly accepted meaning of "hostility to, prejudice towards, or discrimination against Jews.".
The people who prefer to use it with a dash are probably the same people who say "Arabs cannot be anti-semitic as they themselves are semitic". So I looked up and even Wikipedia say that Semitic people is a now obsolete term. Instead we are talking about Semitic languages.
So semitic does not refer to a type of people of some similar origin. It refers to the language. Antisemites are not against languages. They are against Jews. Jews as a religion or Jews as a ethnicity, or Jews as a nation.
Antisemitic Jews
Besides the linguistic point, I find the claim that "Arabs cannot be antisemitic" totally ridiculous. We even know Jews who are antisemitic or, if you feel this is too judgemental, then Jews who express antisemitic thoughts and who display antisemitic behavior.
Antisemitism
So this means that the proper spelling should be without the dash as the word does not mean "against Semites", but specifically "against Jews".