I wouldn't say these documentaries have "changed the world"; but they certainly had a larger-than-usual impact:
"An Inconventient Truth"
Wikipedia: "Since the film's release, An Inconvenient Truth has been credited for raising international public awareness of global warming and reenergizing the environmental movement"
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https://en.wikipedia.org/wiki/An_Inconvenient_Truth>
"Killing for Love" aka "The Promise"
... about alleged murderer Jens Söring -
Wikipedia: "Chuck Reid, one of the original investigators of the Haysom murders, has occasionally agreed to be interviewed about the case. His participation in the 2016 documentary The Promise led him to take his long-standing doubts about the outcome more seriously." Jens Söring returned to Germany two years later.
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https://en.wikipedia.org/wiki/Jens_S%C3%B6ring#Documentary>
In general, I would say it's very hard to pinpoint real change to a particular movie, apart from bringing public attention to some issue. For documentaries which have done so, I suggest looking at movie awards, best of-lists (e.g. BFI) or the National Film Registry in the United States.
