Sisko spoke of "black people" because he knows his history, since it's something of importance to him. He also knows all about the sanctuary districts of 21st century North America and the great social change they brought in as well. In early TNG Picard was a staunch Frenchman, defending his culture. Uhura spoke Swahili. People are influenced by their culture, heritage and history in various ways. Sisko highlighted the injustices of 1960s Las Vegas due to the social exclusion and in his own life teaches Jake to embrace all other species and cultures equally, because what he know of the history of his race has coloured who he is as a person.
He didn't say "black people", he said, "our people", as if there was still a clear separation between "his people" and the rest of the world!
Even the idea that in "enlightened" 24th century they'd still be people with completely black or white ancestry is absurd. Very few people can make that claim now! and they can only go back five or six generations at most. To someone of the 24th century, it should be virtually impossible. So for Sisko to talk about "our people" as if there was an interdict in effect about interracial marriages is insane.
The whole racial thing about DS9 is backward anti-logical nonsense! Come on! People are having children with people from other PLANETS! and Sisko is STILL going on about "our people". That's ridiculous!