Orthodox Magyars are easy. Stephen I turned towards the Pope and the West for a crown and converted to Catholicism because he saw it as the best way to ensure Hungary's survival as a state. I see no reason why he wouldn't have turned to the Byzantines and the Orthodox Patriarch if, in a slightly different situation, Orthodoxy had been seen as stronger. I mean, there was nothing predetermining what religion pagan Hungary would switch to since it was located right between the two religious blocs, and it was also at odds with the Catholic HRE all the time.
How long have the inhabitants of the Pannonian plain been Christian? Wait, who lived there before the Magyars?
The Magyars kicked the Moravians out starting from 896, and Stephen I converted to Christianity shortly before 1000, but it is not known when exactly he converted (there are conflicting sources and contradictions).