Usually, when I read about most empires, the picture one gets is that they demanded political obedience and economically exploited their subject territories, but were not particularly interested in demanding religious conformity or adoption of their cultural norms. Over time this may have tended to happen (e.g., Roman territories adopting more and more Latin culture, Umayyad and Abbasid territories becoming increasingly Arabized and Muslim), but the Romans didn't quickly demand every Egyptian stop worshiping Osiris^1 (nor did their Persian or Macedonian predecessors), the Umayyads were not eager to have the Egyptian rapidly convert to Islam, the Mongols were largely indifferent to whether their subjects were Tengriist or Buddhist, Christian, or Muslim, etc. The British didn't try to end Hinduism. Even the Crusader States, in spite of being explicitly justified by Holy War in their inception, don't seem to have been particularly interested in converting their Muslim or other non-Catholic subjects to Roman Catholicism en masse.
The Early Modern Spanish seem to be something of an exception -- at least, after about the Alhambra Decree^2. When they conquered, they usually demanded that their new subjects quickly adopt Catholicism. Aztecs were expected to very rapidly give up Huitzilopochtli for Jesus, etc.
How unique were the Spanish in this respect? Were there many other empires which attempted to impose the degree of religious conformity on freshly conquered territories that the Spanish did?
(Note: I am not 100% confident of all of the assertions I am making, but I am not trying to perpetuate a Black Legend framework of the Spanish empire. Religious tolerance is not the be-all, end-all of humanity or decency. The Mongols were religiously tolerant, but that doesn't necessarily mean their empire was more humane than that of the Spanish.)
I realize that this changed around the time of Theodosius with actual bans on all pre-Christian religions (whether it was the pre-Christian faith of Italy, Egypt, or wherever), but this was rather later in the empire, not during initial conquests.
Although prior to this they seem to have come closer to following the more common imperial practice in the form of convivencia
The spanish conquest of america, and the conquerors by extension, was heavely influenced by the reconquest of the islam territory in spain, even more it was considered like the continuation. What that means? the main point or at least the justification was the expanse of the christian and catolic faith, even if political or economic power where in the game. Bernal diaz del castillo mentions monks who traveled whit the conquistadores and some papers who they must read to the natives that state they come in the name of the king of spain and demand to accept the chritian faith(in the first years the catolics kings where: fernando vII and isabel) who had all the powers given by the pope to expand the catolic faith to the new lands. So politicaly spain was obligated to do so.
Furthermore, following this, in the explorations monks and his organizations allways followed the explorations of the new lands making them one of the most important tools of conquest. Why? because they educated the natives to the way of catolicism and the european ways of living.