Depends on the family member. My dad introduced me to Star Trek way back in the sixties, but I'm not sure my mother even knows the difference between Star Trek and Star Wars (although she proudly displays my books in the living room). As for my small army of siblings (and nieces and nephew), you've got the whole range from total indifference to casual interest to serious enthusiasm.
By coincidence, my youngest brother started exposing his kids to TREK just this week. I've been helping him pick out kid-friendly eps of TOS like "Arena" and "Shore Leave."
(I gather the Salt Vampire in "Mantrap" caused some bedtime issues!)
As for friends . . . well, I've spent pretty much my entire adult life in scifi fandom, so the vast majority of my friends are heavy-duty fans.