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This would mostly be ASB but what if the 19th Century sees a trend, that of the rise of several religious heterodox movements as major powers?
Mormonism somehow becomes more popular among Americans and finds an extensive following in the western US. This leads to the establishment of a Republic of Deseret that stretches from Utah to California.
In China the Taiping launch successful expeditions to Beijing and Shanghai and pincer into the center of the country, finally overthrowing the Qing and establishing the Heavenly Kingdom's hegemony over China.
The Mahdist regime in Sudan somehow beats back the British and the Turks and eventually conquers Eygpt.
Is there anything else to add to these heterodox movements to truly make it a "Heterodox world"?