And historically if they disagreed well there's that Inquisition Thing to help you get your head straight. Good times right?
The good times in the rest of Europe were the people requesting a hearing/inquisition from the church when secular authorities accused them of heresy, then a crime against the state. Why? For the most part, The Church was considered much more lenient that secular hearings.
Then came the Spanish Inquisition
Tomás de Torquemada
Ferdinand and Isabella
Conversos/Marranos
Muslims
Pope Sixtus and Pope Innocent
The inquisition in Spain controlled by Spanish authorities. Why?
As always, it boiled down to power, wealth, land. Popes Sixtus and Innocent complained about how Spanish authorities were handling their Inquisitions. Unfortunately for later generations of Catholics, one Catholic Friar, Tomás de Torquemada had the ear of Ferdinand and Isabella (had arranged their marriage) with an eye for two regions to unite and defeat Muslim invasions.
Meanwhile, an earlier forced conversion of Jews who became successful and wealthy Christians (and who now held positions of power) had to be ostracized to make room for those who came from older Christian families. So they were accused of being Jewish spies.
Friar Tomás de Torquemada had his hand in all of this. Naturally, Ferdinand and Isabella appointed him the Grand Inquisitor and despite the complaints from Rome, managed to become the man who was responsible for the most Inquisition deaths, possibly more than all other Inquisitions in Europe combined.