Not accurate, People were generally not conquered and forced to convert. After it was legalized in the Roman Empire there was a slow increase in official support for Christianity and suppression of pagan religions leading people to convert out of self interest. Sometimes the ruler would decide to convert and then force the populations to convert. For the Natives in Spanish America it was "conversion or slavery". While later European colonial expansion, conversion was the work of officially supported missionaries and the locals often converted do to the superior technology of the Europeans convincing them that Christianity was superior.
Also, the theme IS accurate about mohammadenism.