To answer the question, . . . Snowden . . . "Why should Black people care?"
I don't presume that Black people don't care, but I do believe that to Black people, at least African Americans, what Snowden has to say is just not 'news' to us, because we have always lived under surveillance in this country, both covert and overt. The Civil Right Movement, The Black Power Movement, and Racism, especially, opened African American eyes, and keeps them open, to how fleeting and fake the Liberty this country espouses can be.
African Americans have been living under a Police State all along, Snowden is not telling us anything we did not already know. But, of course, White racism has always keep the 'majority'/White people, from seeing that the abuse of Black people's rights has always just been the tip of the iceberg of what is to come, dependent on who's wielding the power in this country at the time.
They use Black people to socially condition White people into accepting the usurp of civil liberties, constitutional rights, and a fair and an impartial justice system. When Whites awaken from the racist stupor they have been inoculated with by right-wing politicians and fringe groups, it will already be Law, that also applies to all of them.