Mostly they affected it through their imperialism. They would colonize and take over countries for resources, and with them they would bring their technologies and things that they needed. After they left these things stayed, things like telephone and telegram lines and similar things. Culturally, they would mostly disregard the local culture and impose their own which would often be accepted and kept by the locals, but often there was also warfare.
For decades prior to the Prohibition (i.e., the legal ban of alcoholic drinks) made possible by the Eighteen Amendment, different Christian churches and organizations had been objecting to the consumption of alcohol since they considered it as the source of most debauchery and moral decadence. Their goal was made clear to the federal government: alcohol should be completely banned in order to clean society up. An excise tax on alcohol would have been rejected by all the moralistic groups advocating for prohibition as a mild and ineffective measure
England honors king Georgia
Some religions were banned for political reasons.
Other rites which involve human sacrifice were banned.