This is a thought that occurred to me talking to my wife, who is extremely culturally literate but not (specifically) a Star Trek fan. She would, with sufficient persuasion.
But in a general conversation about Star Trek, a basically culturally literate person will know who Kirk and Spock are. They'll probably know Data, if we're talking about the true pop culture nerds that make up just about all of my friends. Picard is played by a legendary actor, and thus carries enough cache to break through. But then, we get to: the Riker Line.
William Thomas Riker is not a famous character. If you bring up Riker, if you reference Riker, if you call him "the Riker of the West Wing," you will only be understood by Star Trek fans. If you're talking about Sisko, or Worf, or Miles O'Brien, you're past the Riker line. But you can mention the Vulcans in relative safety.
There are a few very minor moments where the line is permeable. You can refer to "Scotty," perhaps, but "Montgomery Scott" is too far. You can talk about Nichelle Nichols work as Uhura being praised by Martin Luther King Jr. for having an interracial kiss with Captain Kirk, but that's about all you can know about her. Geordi LaForge gets you only as far as the visor and the treasured name Levar Burton, but not his work as an engineer on the Enterprise. But fundamentally, anything more obscure than Commander Riker gets you across the line.
But this makes me think of what other pop culture spheres have their own Riker Lines. I'd put Harry Potter's Riker line at Neville, I think. Star Wars line is at Bobba Fett. I haven't seen Lord of the Rings through, but whoever comes after Legolas fits the bill. Any others?