A few muddled thoughts on this from my experience:
as others have said it really seemed to erupt after 9/11 (though due to my age I wouldn't really remember it before then anyway), but as you rightly point out the weakness of the left and I think its alienation from the working class and the neoliberalisation of sections of it prepared the ground for the right situation to bring it out into the open.
Neoliberalism and the mutual turning away of the working class from the left and the left from the working class paved the way for an individualised politics concerned with the moral failings of 'elites' and an alienated world view leading to the key question of why everyone else can't see what the 'leftist' can. It's a breeding ground for classist conspiracy theory. Some of the ingredients are ever present among the liberal left - the brainwashed masses reading the Sun or the Mail etc, the liberal obsession with cobbled together 'facts', and smug explanations going even so far as to assert that 'right wingers'/'conservatives' are genetically disposed to reject them. Politics can become transformed into a comodified individual awakening.
It seemed as though the legacy of cold war anti imperialism provided the initial focus for its expression post 9/11, with the war on terror, the wars in Afghanistan and Iraq etc. Obviously the 9/11 Truth stuff, but also a wider tendency where the decayed remnants of global socialist/working class struggle became warped and re expressed in all kinds of bizarre ways (suspect there was always this tendency, but now the counter influences have to a large extent vanished). I remember contorted leftist defences of Ahmadinejad. This is where I first encountered it I think - with what I thought of at the time as uni student Chomsky fans who liked posting links to znet. Stop the War/Respect provided another wing.
Another strand is Anonymous, which in my view has been quite important in normalising conspiracy theory and to a degree anti semitism. The development of Anonymous has strong roots in 9/11 conspiracy theory and right wing anti semitism/racism, both seriously and as a 'joke' of sorts. Early exposure arrived through the Jews Did 9/11 website which got them on Fox News as I remember, as well as racist/sexist etc trolling. The Ron Paul presidential campaign in 2007/8 provided another opportunity for right wing conspiracy theory to coalesce within Anoynmous and an early venturing into overtly political action. The left wing version such as it is kind of arrived with the anti-Scientology protests which were around the same time as the Ron Paul campaign. It then ventured into various other protests, and there was related stuff like the LulzSec hackers (and an FBI informant), which again I remember leftists defending and getting excited about, in spite of their attacks against ordinary people.
The point with that is that whereas I don't think all Anonymous members/supporters are anti semitic, it has roots in it and conspiracy theory more widely, but also it emerged from an internet culture where anti semitism was (and likely still is) rife, and where it was virtually never challenged, or what challenges there were got attacked as by 'outsiders'/'fags' who didn't get the joke. So I think it was normalised, and where Anonymous has been incorporated into the wider liberal left that normalisation has followed to some extent. This was visible in Occupy etc, where you may remember the Ron Paulist/libertarian right wingers and the more leftist incarnation were both present (at least early on), both at times united around crank money theories and anti semitic banker stuff for example.