Ms. NICHOLS: Well, it's interesting that you said, you know, you would run through the house and look. I met Whoopi Goldberg when Gene was doing The Next Generation and she had told me when Star Trek came on she was nine years old and she said she turned the TV on and saw me and ran through the house screaming: Come quick, come quick. Theres a black lady on TV and she ain't no maid.
I vividly remember one of the TNG documentaries with a Whoopi Goldberg interview and this ^^ is exactly what Whoopi Goldberg said for word for word.
Now either Whoopi Goldberg has memorized this anecdote (and just "replays" it every time she has a chance, which I personally do not believe) or Nichelle Nichols didn't remember the exact wording and chose to copy and paste the text of the interview, instead.
Other than that I have absolutely no doubt, that Dr. Martin Luther King, Jr. felt about Star Trek the way it has been presented here.
According to Whitfield's Making of Star Trek
(and the context of the time in which TOS was produced) "By putting a Negro in the crew they might lose the Southern states, by putting a Mexican in the crew they might lose Texas, Arizona, and parts of California, and so forth."
I don't know if that has been properly acknowledged but unless I'm mistaken the second other starship captain in production order featured / mentioned was an African American!
Commodore Stone (Percy Rodriguez) in "Court-Martial" (produced before "The Menagerie" and Captain Pike) explicitly mentions that he had been a starship captain (and in this episode obviously outranks Kirk).
In the airing chronology Commodore Stone was the second character to have been a starship captain (Pike being the first) and "Tomorrow Is Yesterday" suggested there are only 12 (prestigious) starships like the Enterprise
"Court Martial" was the episode broadcasted right after
TY so I can imagine how excited African American audiences (possibly including Dr. King) must have been, that an African American had previously been captain of one of these few 12 starships.
So I could understand that Dr. King saw quite some potential here and asked Nichelle Nichols to stay.
Of course, it took until 1982 until we finally saw
an African American captain of a starship.