Indigo, I would like to charitably suggest that you do some research on the Spanish Inquisition.
The Church could not execute anyone. What the Inquisition did was to try those accused of heresy. This was necessary because there were people who falsely converted to the Catholic faith while working to undermine it, and Queen Isabella would have none of it. At one point, Queen Isabella did expel the remaining Moors from Spain - after a revolt that took place subsequent to the completion of the Reconquest.