OTL it took until last year to have a black female captain in a Star Trek franchise (Burnham in Discovery.) The question is, between 1969 and 1987, would there be enough demand for another Star Trek series? It wasn’t a hit until syndication, so in the late 1970s, could people bring it back the way shows like Family Guy were brought back in the 2000s?
Bear in mind that, in 1968, Kirk and Uhura kissed on screen, one of the first instances of an interracial kiss. It didn’t destroy the show (shitty ratings did.) And I know that, in the 1970s, TV was starting to cater to the black community. So it’s possible it could work, but you may be averting a few things here - Nichelle Nichols was very influential in getting Sally Ride into space, so that may be lost.
On the other hand, Barack Obama’s is a Trekkie, so a show like this would make him an even bigger nerd.