There's a small, politically motivated subgroup of people (not saying you are one of these people, just that you are buying what they are selling) who want to cause confusion by screwing up a perfectly well known word. You know what antisemitism means when someone uses it though. So do they. They just don't like being called an antisemite, so they try to f up the word.
There's a difference between gay and splitting off semitism from antisemitism. It's that gay is a single word. "Antisemitism" is a single word. It's like complaining about "Irregardless". Yes, technically, you can break down the word to "not without regard" = "with regard", but it really means "without regard".
Language does not work via lego blocks. Homophobia doesn't mean fear of gay people. Nor does Islamophobia.
Terms start from weird places, even hateful ones. It doesn't really matter though, what matters is how it is used.
