That’s how things are bearing themselves out.
There is also another tactic of the ethnic antisemites who try to convince the religious antisemites, that being the false claim that the Jews who went to the state of Israel are actually not ethnic Jews but Khazars. The real Khazars were a Turkic people who inhabited the Caucasus and built an empire that stretched into modern-day Ukraine and southeastern parts of Russia.
That's just bats. I'm familiar with the Khazars: they weren't ethnically Semites at all, but an unrelated nation that adopted the Jewish faith.