As far as I can see, Hungary at that point still had most of the trappings of a Constitutional Monarchy, along with some Fascist characteristics from the military overthrow of the brief Communist coup. It was not quite Monarchy, not exactly Fascism, and only somewhat Democratic (mainly at the more local and regional levels), with restricted access at the national level barring ethnic non-Magyars from holding higher offices, but no official restrictions on education or political involvement at the local level. While there was some support for both Communism and National Socialism (as in most other countries at the time), those were both being suppressed to varying degrees by the government.
One of the more heavily Nazi-leaning officials was eventually discredited (much to the relief of most of the government) when it was discovered that his grandmother had been Jewish, not that being Jewish was a problem (there was at least one Jewish Cabinet member), but that the Nazi racism thing came off as ridiculous coming from someone who was partly what he was ranting against.
Quite simply, Hungary doesn't fit squarely into any of the neat and tidy categories which the game shoehorns various nations into. Poland likewise doesn't quite fall into the "Fascist" camp, and Romania was clearly not the ideal of Democracy.
I think that HOI3's political representations had the potential to be far better, but the game failed to make those distinctions relevant in the actual game mechanics, particularly with regard to the degree of cooperation, political drift, and other factors. In my opinion, making Conservative and Democratic Socialist parties provide a slight bias toward their own ends of the political spectrum, and a slight bias against the opposite form, would have been much better, rather than treating them all identically. Example: A Conservative party could have only 80% of the normal drift toward a Democracy faction and 20% toward the Fascist end. Democratic Socialists might only get 80% drift toward Democracy and 20% toward Communism. An Authoritarian state might only get 80% drift toward a Fascist faction, and 20% toward Democracy, while a Radical Socialist party would see an 80% drift toward Communism and 20% toward Democracy. That would have made adjacent forms of government tend to act a bit more alike, rather than having an ideological chasm between the 3 basic forms of government.
Hopefully, the inevitable Expansions for HOI4 will include something more realistic for the political end of the game.