I haven't read the book, but based on the general shape of argument, which I'm extremely familiar with as I hang out with lots of leftists, lots of Jews and lots of leftist Jews: Baddiel is right that many on the left regard anti-Semitism as an acceptable prejudice or think it doesn't really matter (crudely, because British Jews are usually white and on average richer than the general population). Corbyn I'm pretty sure is in exactly that position, he doesn't hate Jews personally, he just thinks anti-Semitism isn't serious.

However it's almost always a mistake to talk about a prejudice being acceptable by contrasting it with another prejudice that you think is taken more seriously. Much of the British left, within the Labour party and in traditional as well as social media, is extremely tolerant of, if not actively participating in, transphobia. It's like when someone says "nobody would ever say / do that to a Black person"... the reaction is universally, er, actually people do say and do that kind of thing to Black people all the time.