"Conquistadores getting in trouble with the Priests and Bishops"..............These clergymen accompanying the Conquistadors were similiar in form and function to the Commisars of the Red Army. There was no such equivalent with the English/Scottish (Anglo/Celtic)conquerors of North America.
You think that the Commissars were there to restrain the Red Army? You got another think coming.
In those expeditions under the official sanction of the crown, probably. However, many times it was band of adventurers that started out alone. There is a reason that the governors of Santa Fe got replaced often, they kept running off looking for gold