It’s my understanding that those Israeli neo-nazis have at least one Jewish ancestor. The fact that such a person living in Israel can become a neo-nazi still sounds absurd to me.
My only point is: Strange things do happen. But the suspicions about this group should be completely warranted.
There are thousands of Russians without Jewish ancestry (”at least one ancestor” is also rather vague and hard to prove) that have entered Israel and also Germany because of favorable conditions on the pretext of being of Jewish origin. Jewish emigration offices profited from bringing large numbers of emigrants from former Soviet states, so they let in also non-Jews. It’s a rather well know problem in Israel.