The Hungarian tribes were largely pagan when they 'settled' in Hungary under Arpad and it wasn't until his Grandson Geza that christian Missionaries were allowed into Hungary. Specifically Missionaries from Western europe, as this was largely a move to placate the Holy Roman Empire under Otto I, who had a marriage Alliance with the Byzantines. The simple fact that Catholic missionaries were allowed in eventually led to a somewhat rapid conversation of Hungary over the next few rulers, Specifically King Saint Stephen of Hungary who founded several monasteries and Bishoprics in Hungary all affiliated with Roman. So by the time the Great Schism happened Hungary was already had closer ties with Rome and it's immediate neighbor the HRE and was from a religious perspective squarely under the influence of the pope.

So in a sense Hungary didn't become Catholic, Rather it was Catholic from the start of Catholicism being it's separate branch.