There are two main arguments about Hungary 1956 being primarily anti-semitic/nationalist:
1. That the Hungarian Communist Party was mainly jewish, and therefore the 1956 uprising, because it was against the Communist Party, was an anti-semitic pogrom.
This doesn’t really merit any discussion and google only really finds David Irving pushing that narrative, although tankies on twitter do it too. I did find this LRB review of 2006 academic books which discusses it a bit: https://www.lrb.co.uk/v28/n22/eric-hobsbawm/could-it-have-been-different
2. That Hungarian Nazis (possibly backed by the CIA) were involved in the uprising. I don’t think anyone disputes this, the question is the extent to which they were involved, and to what extent this has anything to do with the factory committees etc.
mirysics’ post is arguing this second point, and there are some facts provided in his comment, just not much. I think it’s better to engage with what’s provided than just dismiss it though, so here’s an attempt:
“Freedom fighters” such as Béla Király, Gergely Pongrátz, Ekrem Kemál, the entire makeup of the anti-Soviet forces in the Battles of Corvin Köz, Széna tér (the two most significant and largest anti-Soviet fronts), these people were fascists.
Bela Kiraly was proper Hungarian fascist officer – he commanded a forced labour jewish battalion in WWII http://www.independent.co.uk/news/obituaries/bela-kiraly-soldier-who-led-hungarian-resistance-against-the-soviet-union-during-the-1956-uprising-1741949.html
Gergely Pongrátz – no politics in this obituary:
http://www.independent.co.uk/news/obituaries/gergely-pongraacutetz-5345541.html
Ekrem Kemál I can’t find anything in English, although his son (similarly named) was a Nazi.
Some more googling, and I found this declassified CIA document on the Hungarian Freedom Fighters Association, identifies several key players as fascists: https://ia601305.us.archive.org/0/items/HungarianFreedomFightersAssociationINSCOMDossierZF010456WJ/Hungarian-Freedom-Fighters-Association-ZF010456WJ.pdf
So the leadership of the main nationalist military units in Budapest were Hungarian WWII veterans and likely many under their command.
However this does not at all explain the student and workers councils, which were in all major cities, not just in Budapest, and which continued for weeks after the military resistance had been crushed and any fascists involved had fled Hungary or well on their way.
Also in Budapest itself a lot more was going on than these groups. Sandor Kopasci, who was in the communist anti-fascist resistance during WWII rose to become chief of police in Budapest, joined the revolt (in Nagy’s circle), ended up as a janitor in Canada. I read ‘In the Name of the Working Class’ (didn’t realise he was the chief of police until after I bought it..) a few years ago and he talks about going to meet anarchists in the city centre briefly, people he would have arrested weeks/days earlier.
So there was obvious Hungarian nationalist/fascist involvement, but this is used both by tankies and the Hungarian right to try to limit an understanding of 1956 to their involvement, ignoring everything else.
This shouldn’t be either dismissed or over-emphasised, but it needs to be put in a proper context and to be honest I haven’t seen a good attempt to do that anywhere. https://libcom.org/library/hungary-56-proletariat-storming-heaven-mouvement-communiste for example says right at the start it’s not going to even go into the question, but then it’s discussing the movement in the factories rather than the streets.
