Yeah, I would never assume that someone harbored any kind of antisemitic prejudices just because they happened to be Muslim.
However, the pervasiveness of anti-semitism in the Middle East may be relevant in the whole Ilhan Omar controversy. But that whole thing is super complicated, and I wouldn't assert with any degree of confidence that anything about how her background informs public comments that she's made.
Yeah, well, regimes in the Middle East often use anti-semitism and anti-Zionism as a scapegoat to distract from their own abusive policies towards their own people, so it's effectively a state-endorsed policy. Like, even Egypt, whose government has made peace with Israel, and which has even cooperated with the Israeli Air Force to combat ISIS in the Sinai, still widely disseminates antisemitic material through its media, because pointing to the "foreign threat" helps to maintain internal solidarity. In quite a few Arab states, there's a real gap between public opinion on the one hand, where hatred of Jews and Israel is widespread largely because the public has been fed on government sponsored anti-semitic propaganda for decades, and, on the other hand, the views of their governments, which see Israel as a potential ally in the region in the broader regional conflict with Iran.
It's really bad, in part because it means that any strides that Israel has made with Arab allies in the region is fundamentally premised on the disenfranchisement of the people who actually live in those countries, and therefore, on ensuring that they remain autocratic. If they were democratic societies, they'd behave in a profoundly different way.