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King was definitely not protesting in a rules based order, at least not one which applied to black people. Nor was Gandi.
We haven't had a 'world order'. We've had the threat of mutually-assured destruction.
Which has prevented another world war, but not regional conflicts, a cold war, and whatever the history books decide to call the current social media driven conflict.
I share your sense that there is an unsettling in the balance of the world order at present. However, I completely disagree that non-violence has no place in the absence, and I enter into evidence the Satyaagraha movement in British India in the interwar period, especially the leadership of Mahatma Gandhi.
For just one example, see his response to the Massacre of Jallianwalla Bagh, which happened around the time of the end of WWI.
https://www.mkgandhi.org/storyofg/chap18.php
Non-violence formed a backbone of the Indian independence movement until independence was achieved at the close of WWII in 1947.
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As long as you pretend these didn't happen:
Iran (1953) - overthrow of the Shah by the CIA
Guatemala (1954) - overthrow of an elected government on behalf of US corporate interests
Cuba (1961) - invaded Cuba via proxy forces, attempted to assassinate Castro (Bay of Pigs)
Vietnam, Laos, Cambodia (1955–1975)
Chile (1973) – overthrow of Salvador Allende
Nicaragua (1980s) - overthrow the Sandinista government (Contra war) without international authorization
Panama (1989) - invaded and overthrew the government without international without international authorizationauthorization
Iraq (2003) - invaded and overthrew the government without international authorization
Serbia (1999) - airstrikes without international authorization
Libya (2011) - exceeded authorization by UN to effect regime change
Syria (2014–present) - US military occupation and oil seizure is ongoing
There are many more, these are the more notable ones