ZOG isn't an embellishment of the truth, it's a full-blown conspiracy used by white supremacists. ZOG doesn't mean that zionists have a strong lobbying influence, it means that governments are controlled by Jews. Framing it as partially true validates white supremacist conspiracy theory.
Zio- also has direct origins to David Duke, the Grand Wizard of the KKK, which he uses as a dogwhistle to describe Jews and the zog conspiracy. Neo-Nazis and white supremacists use zio- as a pejorative dogwhistle, don't try to change it into something else, or even use it, that just gives them validity, it allows them to hide behind you.
The latest chapter in the Chicago Dyke March controversy unfolded late last week after the group walked back its use of the term “Zio,” a pejorative brought into prominence by former KKK Grand Wizard David Duke and often deployed by white supremacists.
You're also drawing a false equivalence. People volunteer to be MAGA, they don't volunteer to be Jews. I'm not saying that zionist automatically equals Jew, I'm mentioning that ZOG and Zio- are antisemitic due to their history and what they mean. And when those in conjunction with "death to Israel," it looks more like you're using antisemitic dogwhistles and referring to Jews instead of Zionists.