I think what I proposed is a factor, but it does not explain everything. While the medieval decentralisation of Germany, Italy, or even France (where Burgundy could wage war against his liege and it was not really seen as something abnormal, or how pairage / peerage meant in a sense being equal to the king), Hungary was about as Catholic as it comes and yet it was more centralized, at the very least beginning with the Anjou era in Hungary, Caroberto. In fact the Hungarian pattern seems similar to the Eastern Orthodox one, just Catholicized. E.g. at 20th Aug the birthday of the country the embalmed right hand of King Saint Stephen is carried around in a procession by bishops. A very clear unity of throne and altar.

I think the chain of causality is closer to factor X -> decentralisation, weakening of state power -> religion keeps some distance from the state, rather than religious statism preserving the strength of the state. But I have no idea what the factor X may be.