I don’t believe that the church at that time actually believed as a matter of doctrine that there was a divine right of kings, but allowed the concept in order to keep the various monarchs in line.
I think it was more along the lines that kings supported by the church acted in the name of God, Christ, and the vicar of Rome. It was tolerated as a rule as long as it did not impinge on the actual control the church held over much of what went on and how life was conducted. If a monarch stepped outside of acceptable bounds they were threatened with excommunication which would lose them support among monarchs who held to church doctrine.
Henry VIII put the divine right concept and the power of the church on a downhill slide when he defied Rome by divorcing his wives and establishing his own religious doctrines. It took a while but the real political power of the church to control kingdoms and raise armies declined after that point.
The difference was that the Catholic Church always viewed the Church and the State (that is, the King) as two separate entities, even at times when the Catholic Church was the official state church. The Church, in fact, often ended up opposed to the civil power, even though it was often simply pragmatic - because the civil power (the King) had decided he wanted to seize Church properties or take over powers and property from bishops or abbots.
Collusion or accommodation between secular and religious powers is never good, but it’s different from a theocracy, where the King (or civil authority) is also a religious figure and gets to be in charge of both aspects of his subjects’ lives. That was what Henry VIII introduced, and what the Church opposed.
Luther saw according special status to the Crown as a way to gain power for his movement, and of course, Calvin was a genuine theocrat, and envisaged a society where the civil and secular powers were one and the same. The Puritans (Calvinists) who came to the US had this in mind, but after a mini-reign of terror in their area, their project didn’t last because it’s simply unsustainable in Christianity. (Islam, however, does operate on a theocratic basis.)