STAR TREK was not required to inspire MLK on his mission for equality.
No, but it helped promote his ideas. Fiction may not be "needed" or "required" or other such gratuitously exclusionistic terms, but that doesn't mean it isn't
valuable in spreading ideas. After all, if you want to promote a belief, you need to communicate it to the people and convince them that it's worth buying into. Sure, you can do that with speeches and news articles and the like, but you can
also do it through fiction, and it's foolish to dismiss that vector for spreading ideas out of some elitist notion that fiction is somehow unworthy.
But if NASA wasn't so aweful at Public Relations on its own, it wouldn't need celebrities to help push it.
Again, it makes no sense to treat it as some absolutist, zero-sum choice between the two options. It makes the most sense to use
both approaches.
STAR TREK was never known for its "cool" factor, until the reboot. Let's not pretend about that. Yes, the show's been popular for decades, but during most of that time, fans were branded as friendless geeks, living in their parents' basement, going to work in their "uniform" and making everyone call them "commander."
Among the general public, yes. But those "geeks" you're talking about are the kind of people who would be inspired to become scientists and engineers and astronauts, and we know that many of them were indeed inspired by
Star Trek.
Right now, NASA is pursuing proof-of-concept experiments for what's called the
warp field interferometer, a test of a theoretical method for warping spacetime in a way that could hypothetically lead one day to real stardrive applications. The idea of a warp field, once dismissed as unachievable, has been taken more and more seriously by theoretical physicists ever since the pioneering work of Miguel Alcubierre in 1994, in which he calculated how to solve the equations of General Relativity in order to create a spacetime metric that would behave as a warp drive. While it required physically impossible states of matter and amounts of energy, later theorists have found possible ways around those problems, so now we're to the point that it's taken seriously enough to have crossed from abstract theory to the first tentative experiment. If this pans out, we may someday, in the distant future, have an actual stardrive -- if not FTL, then at least a greatly improved sublight drive. And it will all be because of Miguel Alcubierre...
...who is a major
Star Trek fan and has acknowledged that the show inspired him to devise his warp metric.
Of course, that's still pretty much pie-in-the-sky, but there's a long history of real-world
inventions inspired by science fiction, from the submarine to the taser to the mobile phone to the computer virus. The relationship between scientific progress and science fiction has long been a mutual symbiosis, with each inspiring the other. After all, science progresses through the communication of ideas, and fiction is an effective way of doing that.