The colonization made in Latin america made this close to impossible, unless some european colonizer purposely decides to build a theocracy in one of their colonies.
The objective of the colonization was basically to take over the land and reach the hightest profitability, this does not change from canada to Paraguay, but in Latin America that means one simple process that is repeated in every single country with just minor changes based on climate and terrain: Monoculture (One main product, grain or cattle in argentina, coffe or cattle in Brazil, sugar cane in Suriname, etc), slavery, great proprierty and only urbanizations close to the coast, or to put it simply, the plantation system. That meant that basically as soon the colonizers left who is going to take power are the oligarchs, it was like that in every single country, even in the ones that had a monarchy like Mexico and Brazil, the King was purely symbolic and who held the power were the oligarchs (maybe not with the first emperor, but as time passed the monarchy burned it's powers to the oligarchy). You cannot have a theocracy because their values are the opposite of a oligarchy.