tbf, every actual neo-nazi is probably doing everything they can to further piss off Israel. It's just a convenient opportunity is all, if someone is actually a hater.
They're not anywhere close to the majority, the majority just wants to save lives. But they're loud and sometimes clever, and good at hijacking other people's causes.
Both anti-semitism and anti-arabism exist, and both are bigotry, because all Jews and all Arabs are not the same, and will never all be the same. Any more than all Americans are the same.
It's a hard world though, right? Means we're going to need something better than simple, easy tools to wrestle with it. That's just how hard it is, and how little it cares about anyone's wishes for it to be simpler.