I believe that Corbyn doesn't hate Jews and in that sense isn't the anti-Semitic person that people claim him to be; however, the whole saga isn't that clear cut.
I see it as that he doesn't care enough about anti-Semitism because he perhaps presume that they're likelier to be richer and more likely to vote Tory/not Labour.
This in itself has allowed and/or facilitated a wider spread of anti-Semitism through the lower echelons of the party, which is where the major issue should lie.
If people think that it's pure press talk and propaganda, I have real concerns; I personally know of a number of cases, to varying degrees in the last year alone.
That's not to say the other parties haven't got their own bigotry and discrimination because they have, but it shouldn't negate the discrimination in another.
I disagree, slightly, with the first bit of your post.
Not caring about anti-Semitism (at least the current definition) is something that almost the entire political class were and are guilty of - look at Boris with Taki, various Labour MPs (including Corbyn) with the anti-Zionist fringe, the Lib Dems with Ward and Tonge (admittedly they eventually withdrew the whip there), Rees-Mogg hanging around with the extreme Tory right and Despatches could put on a show in primetime TV talking about the "Israeli lobby" influencing British politics. I am not saying noone spoke up against it at the time - loads did - but it was not a topic that was the existential threat it is now claimed to be.
This indifference wasn't just about AS either - you'd be incredibly hard pushed to find any example of an MP being dealt with by a party for sexual misconduct before 2015, and what they were doing with expenses was something concealed for years. The Tories ran an openly Islamophobic campaign in London during the last mayoral election.
The change came when Corbyn became leader - people on that fringe did start to join (more accurately, re-join in many cases) and they have continued to bang on about Zionism and pretend the problem isn't them doing that. They have to be challenged, but the outcome of this - and Corbyn being leader - is that a lot of them actually are now. One of the figures I'd love to see is how many Labour members were kicked out for AS before 2015 - I'd be willing to bet a new 10p piece that it is less than it has been since.