Labour's NEC officially adopted the International Holocaust Remembrance Association (IHRA)'s "working definition of antisemitism" (linked below). IHRA provides supplementary guidance, including 11 specific examples, and notes that context is critical in identifying antisemitism and expressions of antisemitism may vary among different cultures, legal systems, languages, etc.
Labour (under Corbyn) adopted not just the definition but the entire guidance, including the examples. Like it or not, that's the standard to which Starmer has to hold his front bench, and RLB presumably knew that.
(Labour's stance on this is controversial - some members wanted them to adopt a different definition, or to keep the IHRA's definition and refer to the guidance without literally adopting it as the rule.)
IHRA's origins lie in groups of Holocaust survivors wanting to educate the public about the Holocaust and its causes and consequences. Their examples include "tropes" that have historically and recently been used to whip up antisemitic sentiment, which has had tragic results all over our continent, within living memory.
The Labour party also has a detailed policy on Islamophobia. If someone wants them to adopt a detailed policy on criticising China or Russia or North Korea or Catholics or trans people or Americans or anyone else, the first step would be to put together evidence about how prejudice against that group operates historically and currently and is damaging/dangerous, and lobby for the party to adopt it.
The problem with RLB seems to be that she and the party did get complaints from Jewish groups who did read what she shared as antisemitic and potentially damaging even if her intent was not antisemitic. Starmer asked her to delete it on that basis, she refused, he asked her to resign. He's not holding the general public - or even Maxine Peake or the Independent - to the same standards.
www.holocaustremembrance.com/sites/default/files/press_release_document_antisemitism.pdf