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I guess Hungarian America would still be nuclear and IT superpower, we had the Jews for that (just think of Teller and Neumann).
In cuisine, Mexican/Tex-Mex would be much more widespread, since pörkölt and chili is basically the same, probably beef-paprika-onion-beans type of foods would be the staple all around. Hamburger might still exist with stronger garlic flavour. Beside bacon, salo type of fat slabs would also be dominant. More and better wine, fruit spirits instead of whisky.
Western movie absolutely would be one of the largest genre, probably country music too.
And now that we are at Mexico, that is also rightful Hungarian clay, so it would be part of the States. No wall there. Maybe on the Canadian border for good measure.
Civil wars and "peace when united under a stronk leader" type eras would constantly alternate. Probably religious wars against Muslim countries in alliance with Poland, Germany would be our total bitch.
> The educational system would have a really hard time teaching students since Hungarian is bretty difficult to learn
Nod really. Second generation immigrants would do just fine.