Australian News

"Hating Jews" is a broad and unhelpful way to frame this.

The article quotes them specifically and repeatedly saying "Israeli", never "Jew", so we can assume they're not discriminating against Jews in general but against Israeli Jews. And that is important to qualify, because in the context of Zionism and the Zionist Regime, there is an important and over-century-long distinction between Zionist Jews and anti-Zionist Jews. It's harmful and antisemitic to assume all Jews are involved in or supportive of the Zionist Regime and its actions, so that's why it's important to clarify that anti-Israel sentiment (anti-Zionism) is different to merely "hating Jews" (antisemitism).

They would call an Israeli Muslim a dog?

In most cases I'd assume not, because most of them are simply Palestinians remaining where they already lived prior to the occupation, rather than colonising supporters of the Zionist Regime who identify as "Israeli", but if they were one of the minority of Muslims or Arabs who declare themselves pro-Zionist then I reckon they would be called a dog no matter what their ethnicity or religion. On the same note, an actively anti-Zionist Jew living in the Zionist State wouldn't be called a dog. It's not about a person's religion, it's about their Zionism, which for historical reasons has strong religion and ethnic bias in the Zionist ethnostate.