14
Based on my experiences meeting other Trekkies at Phoenix Fan Fusion and Tuscon Comic Con.
Like, once you get past this part, most of the original Trekkies are fun to talk to, but combined with that subset of gen X TNG guys who talk about their college years and give you unsolicited life advice while probably a bit inebriated, you probably lose an hour at whatever convention to hearing this same flex over and over again. 
Also, yes, at Fan Fusion I found out Gen Alpha Trekkies do exist; saw one wearing a DS9 uniform commenting at a panel.
I always find it really funny when they guess someone has only watched newer stuff and can't fathom that they've seen almost everything.
I've had the opposite experience online: contemporaries who assume I'm half their age just because I don't think every Trek made this century is categorically trash.