I can similarly post opposite examples. Hence my anecdotal statement.My oldest grandson (15yo) will watch the occasional episode but he's not devoted to it and never asks to see an episode. He regularly asks to watch episodes of I Love Lucy, Leave it to Beaver, and Gilligan's Island but never any drama programs from that era of broadcasting (he's seen episodes of several - Voyage to the Bottom of the Sea, Lost in Space, The Man from U.N.C.L.E., Mannix, Hawaii 5-O, The Wild Wild West, and a few others). He seems to enjoy it when he watches an episode with me so maybe there's hope and I just need to get the right episode(s) for him to take interest.
His oldest sister (12yo) has seen a few episodes of TNG and never asks to see it. If that's what I'm watching she usually leaves the room after 15-20 minutes.
Their sister (7yo) will watch complete episodes of TNG with me but I don't think she's seen any TOS. However, she, like her brother and sister, never ask to watch any Trek. That could easily change if I watched enough of it with her.
All three generally ask for comedy series from the 60s and I'm OK with that as my preference leans in that direction but I'd really like to get them interested in some of the better dramatic series, especially Star Trek.
Their mom, my daughter (39yo), never watched Trek. She might now but I just don't know. I'd have to loan her some seasons with a "watch some and let me know" mandate.
My son (36yo) has watched episodes of TOS, TNG, and DS9. He didn't care for any of them. But he's never been too interested in anything SF related - other than Star Wars (and he's a huge SW fan - skipped school, with our permission, to sit in line to purchase a ticket for the Episode 1 premier at the local theater).
No one I work with (ages ~22-39) watches anything Trek. Most watch the Marvel and DC superhero movies bit didn't bother with any of the "New Trek" movies, much less the older stuff.
I know 2 people who like and watch Star Trek. One is in his late 40s (likes it all), the other in his mid 50s (only likes TNG).