'Jews are controlling the media' isn't antisemitic? 'der Stuermer' was depicting caricature Jews with long noses just for the fun of it? And yes, fictional conspiracies were a big deal in antisemitic propaganda - 'the protocols of the elders of zion' is just an example.
And regarding The Protocols of the Elders of Zion. The whole point of that book is that it was passed off as not being fictional. It was fraudulently presented as a real text.
https://www.theguardian.com/books/2020/dec/06/roald-dahl-fam...
“It’s the same old thing: we all know about Jews and the rest of it. There aren’t any non-Jewish publishers anywhere, they control the media – jolly clever thing to do – that’s why the president of the United States has to sell all this stuff to Israel.”
So just talking about conspiracies isn't a good indicator of anti-Semitism.