A lot, way more than people tend to think. International relations and agreements are significantly different than internal laws proposed through legislation. Typically, treaties are negotiated by a relatively small number of people then submitted to the main governing body for approval. Internally proposed legislation has to pass through many layers of government, pass through many hands which affords significantly more opportunities to derail said legislation.
Operating on the national/international level allows you to recruit other groups and nations to apply political and economic pressure to effect change.
There are a few good examples of this in history (which will be grossly simplified for space related issues)
Apartheid in South Africa, for decades there was official legal repression in South Africa from the white minority. Internal opposition to Apartheid, although significant wasn't terribly effective and largely led to increasing violence from both sides. Now, I've no desire to devalue the efforts of motivated South Africans to effect change but the most valuable thing they did was motivate the outside world. Apartheid came to an end because from the late 70's through the 80's the United States, the United Kingdom, and 23 other nations had passed significant trade sanctions on South Africa. A movement for disinvestment by many more countries was similarly widespread, with individual cities and provinces around the world implementing various laws and local regulations forbidding registered corporations under their jurisdiction from doing business with South African firms, factories, or banks. The overwhelming international political pressure and crippled economy forced change.
Civil Rights in the USA
The 13th amendment was passed on December 6, 1865 and the civil rights act of 1866 that made former slaves into citizens. By the end of the 1870s, violent white supremacists came to power and imposed Jim Crow laws that deprived African-Americans of voting rights and instituted official segregation that limited where blacks could legally walk, talk, drink, rest, or eat. Over the next hundred years there were lots of attempts to effect internal change at the local and state level that went largely nowhere. In the 1950's the black community began policies of direct action to challenge the institutions of segregation. They recognized that they could not effect change from within a rigged system that wouldn't allow them to vote. Their policies were to force supreme court challenges and expose the brutality of segregationist systems to people around the country. The segregationist states by and large did not choose to fix the rampant injustices in their systems but were forced to by federal mandate that only occurred by galvanizing non-segregationist states against them.
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You can find parallels with any product with significant enough scarcity, but that level of scarcity and need isn't something you see in the real world. As we see in the data page however (I know you love them so) is that in the fictional world of the MU, so far so good. The advantages the mutants have is that they are the only source and overt violent action would eliminate the product as well as the people.