My understanding was that the Hungarian church of the 1200s was only superficially catholic.
Is that not the case?
My impressions is that by 1200 it was not the case anymore. MAYBE it was the case one hundred years before but by now, Hungary was firmly Catholic. Of course, until 1204, the Byzantine influence was very great (the crown of St. Stefan was sent from Constantinople...). The Hungarians joined Crusades to Holy Land, the fight the Bosnian Bogomils, they tried to convert the Vlachs and the Cumans to Catholic rite, having more success with the Cumans.
Moreover, I beleive that the Hungarian kings were vassals of the Pope with the Pope heavily involved in the succession affairs (case of Bela iv)...