Religion may play a waning role in peoples' lives in the early 20th century, but it is still a force to reckon with nonetheless. In Age of Darkness, the House of worship forms the spiritual focus of your people, and can also be used to influence their opinions towards adoption of the less appetising aspects of your rule by harnessing the power of propaganda.
For China, Russia, Spain and India, access to Communist politics in the form of State Property results in all houses of worship morphing into Party Centres. Party Centres benefit from not being converted to the enemy should a city fall, and in Russia's case, it can also be used to train some powerful command units.