You can by fairly simple lua methods control who can construct or purchase a given building or unit, however. So long as you fake the game into thinking anyone can construct or purchase the building or unit via the definition of the building or unit in tables <BuildingClasses>, <UnitClasses>, <Buildings>, and <Units>, you can then make your lua code over-ride this and only allow a city following for example Judaism to construct or purchase a building called a "Synagogue" when any city would otherwise be able to construct or purchase the building based on technologies the player has, prerequisite buildings in the same city, etc.
In this case you would not be tying the building to a religious belief as is normally done with religious buildings. This method would also require for all practical purposes that the building would not be purchasable with faith.