Omar was accused of antisemitism – immediately by Republicans, shortly after by members of her own party – and bullied into apologizing. She may or may not be prejudiced against Jews, but even if she is, that wasn't her real offense.
Her real offense was publicly mentioning the irrefutable fact that many members of Congress take their marching orders from a foreign power's lobbying apparatus (an apparatus not, as required by law, registered under the Foreign Agents Registration Act), at least partly because those marching orders come with promises of significant donations to those politicians' campaigns.
AIPAC itself doesn't make direct donations to political campaigns. But AIPAC and other pro-Israel lobbying groups like Christians United For Israel punch well above their weight in American politics, largely by motivating their supporters to financially support and work for "pro-Israel" candidates in general elections and help weed out "anti-Israel" candidates in party primaries.