My parents dont really care. I tried showing my mother, she said she likes it (showed her Parasite), but she would rather watch cop shows and stuff.
My father thinks all anime is hentai. Tried showing him (psychopass) but he got bored and fell asleep.
My younger and older sister use to watch alot of anime with me, but then they found other things more interesting to them.
I am not an obvious otaku.
MY dad introduced me to fist of the North star as well as speed racer and my mum got me a Jump subscription as one of my christmas gifts when I was a kid sooo they are cool with it as long as it never got in the way of school or work.
Still watching those chinese cartoons at this age, tsk tsk
My mum and step dad just let me like what I like. My Dad will just take the piss like he always does (our relationship is just us insulting eachother for fun).
Both my parents think (well most of my family in general) think most of my hobbies and passions (anime, video/table top/board/role playing games, etc) are childish and a waste of time, money, and effort. At best, they are completely disinterested, and think I am odd for never wanting to take up sports. My father especially has always disapproved of how much time I devoted to fantasy novels while never being interested in Bible studies.
My dad watched DBZ, but that was it. One day he told me "You're too old to watch those Japanese cartoons." He said that while he was in the middle of watching the Spiderman cartoon so I was like "Really daddy? You wanna go there?" My mom didn't watch any anime at all. But she played video games and they both bought me Shonen Jump, Shojo Beat, Newtype, DVD's, etc... I think they didn't understand it and thought it was weird, but they accepted it. Same with my siblings. They all just accepted that I'm the black sheep. ^^;;
Well my father and I used to watch DBZ when I was a kid. My mother however would forbid I watch any anime because she thought it was too violent so I had to be sneaky and watch it while she was sleeping lol.
Now where to start? disgust? confusion? pity? and most other emotions that took a hit at my hobbies, my mom especially hated it years after when i showed her the money i make thru my hobbies she was skeptical so i had to bring her to one of my transaction a single mtg card costs around 3,000 and i sold about 3 of it just a fewhours after opening it at my shop! still she was confused so little by little i added more to my inventory to show my entire family i was dead serious about it. so i told her remember those DARK magicians that you took from me and burned it in the trash? guess what it was extremely expensive nowadays cause theres this thing in yugioh called FIRST EDITION and now its very hard to come by! hahaha i could have sold it and bought more inventory!
My dad paid for me to study abroad in Japan last year. I feel kind of bad sharing this considering some of the responses here, but that's how my life is.