Trek is not a period piece, its a sci-fi show that is supposed to be humanities future.
Stranger Things is not a period piece, it's a sci-if show that Is supposed to be humanities past.
Or more usefully, given the time-scales involved and the amount of supposition involved....Robin of Sherwood is not a period piece, it's a fantasy show that is supposed to be humanities past. (You can insert say...Outlander...if you like too.)
It's not about the real setting vs fictional setting...both are fictional settings. There's currently a film set in more or less contemporary Hampstead Heath that has all sorts of laughing criticism levelled at it for not really being very accurate to the actual place, despite being filmed there and based on some real people. It's about the approach. Trek has 700 episodes of future history documented...it has its own milieu and mis-en-scene, in just the way periods in in history do...comparing TOS to Enterprises episodes set on the defiant is roughly the same as comparing Blackadder to The Tudors basically. Comparing TOS to Voyager, is like comparing Elizabeth R to Elizabeth: The New World. This is the sense in which I suggest thinking of Trek as a period piece...I am not saying Trek is real, an actual event that will happen and has somehow been magically transmitted through time (despite what the Starfleet Technical Manual says, with its anachronistic components rendered suitable for us past dwellers.)
I am saying that the approach taken by production teams for many years, and a logical approach taken by us fans, and an approach that serves well going forwards is to approach it as a period piece...go far enough back in history and there is as much certainty and guesswork about what is what as there is going forwards after all...the history of the humble Bra was only recently thrown into disarray by new discoveries.
The dialogue in Trek is often compared, acting wise, to performing Shakespeare...a certain rhythm, terms that are not every day....in its difficulty. It's an approach. A period piece for Treks future is different to say...Buck Rogers. It is the same with Star Wars...Rogue One is a period piece, totally, in approach from the makers. Another good example is Alien: Isolation, albeit in video game form.
Star Trek Continues is even more of a period piece, in that they go as far as the replicate certain limitations, but it is plain to see that it is not a show shot on film in the sixties. It borders on an historical recreation, rather than just the general approach taken by other fan films.
Do you see?
When some daft hippy guitar tutor says 'you've got to treat your guitar like a woman' he's not saying the guitar is a woman, nor is he expecting you to buy it dinner and massage its back after a long day....though he may do, in which case, find a new guitar tutor.