with some trepidation, a question about anti-antisemitism....

[Spider Jerusalem]

5. "Jewish" is not merely a religion.

It denotes ethnicity and culture as well as religion. About half of all Jews worldwide are secular; they're still Jewish. Rejecting religion in general isn't "anti-Semitic". Saying things like "the Jews control the media", "the Jews control the financial industry", "the Jews control Hollywood", "the Jews own Congress", "Jews can't be trusted because they're more loyal to Israel than the USA", IS anti-Semitic. Criticising the policies of the Israeli government is not anti-Semitic; conflating the Israeli government with "the Jews" more generally is anti-Semitic. Criticising Zionism isn't necessarily anti-Semitic; conflating Zionism as an ideology and "the Jews" as a people is.

Basically, anti-Semitism lies in assigning negative characteristics to Jews collectively rather than criticising specific ideas, policies and ideologies. It's not any different in that respect to the tendency among some (especially since 9/11) to conflate Islam with terrorism.