My advice is to always keep it hidden. Only reveal it when asked.
You know, unless you watch nothing but hentai or other things that society will raise a brow at, there's really no reason to keep it hidden 24/7 until approached. Because unless you don't buy merchandise like T-shirts or keychains or other things that you have out in the open (because I know not everyone takes their computer/tablet everywhere they go), someone outside of your home will figure it out eventually by a glance that you like or watch anime, somehow or another. By the "things that society will raise a brow at", that does not apply to every single anime out there. Anime is becoming more and more mainstream, slowly by surely despite being a niche, and thus more and more people are recognizing it. They may think it's all Pokémon or Studio Ghibli (Ghibli films are getting more publicity by being shown in nationwide theaters, they have been since at least
Ponyo), but they at least know what it is.
Now does this mean you should run around shoving anime in people's faces? No, but if you like anime enough, you should be able to show a little bit of your interest. My laptop's screenshare is mostly of anime I've enjoyed watching, though it's not without its own share of other cartoons as well, and since I tend to sit up front and leave it idle during a lesson, people behind me can see the pictures fade in and out. Or if I'm done with work early and am bored, or am waiting for class to start, I have sometimes pulled up an episode to watch. But considering I go to a college full of nerds and at the other building in the student lounge video games or anime are shown very often on the TV, guess it doesn't
really count.
My parents and grandparents know I and my brothers watch anime, and they have watched a few of what we have (whether on my request or because they just happened to be in the room when it's on). But of course, they're cautious of it--which I'm pretty sure a
lot of people had known about all the Japanese porn in the form of cartoons in the 80s and 90s, so that reputation didn't help any for years. However, my mom's grown a little more lenient towards anime after all the Ghibli films and shows Kids WB/4KIDS (and Fox Kids for Digimon) aired, so we have a fair share of a collection at the house, but she is still strict about it. She will not buy an anime without looking it up first, but for the past several months, I've been the one they've gone to to make sure it's appropriate for the younger boys to watch before they buy it. (She took away the InuYasha and Nura DVDs because she didn't find them appropriate, but because the twins bought them and the twins are gone right now, they're just in their closet.) So it's because of my interference that we have the anime we have right now, but I'm not sure if that's
really going to stick when I eventually move out of the house. They don't necessarily trust the twins because they've watched their share of stuff that Mom doesn't approve of. (Dad's much more lenient, but he has no interest in watching one unless he's really bored enough to put something in--like he did years ago with the Escaflowne movie.)
So anyhoo... yeah. I'm not afraid to show I'm an anime fan, I just know my limits. If I feel my mother may like an anime, I will ask to watch it with her, and thus far we've watched CLANNAD/After Story, Escaflowne, and Kanon together. I've even watched CLANNAD with my grandmother, and she ended up liking it, and we recently saw
The Wind Rises together because she knows how much I enjoy anime. (She liked the movie--and there were more old folks there than young folks despite being a small audience. They all stayed the whole two hours.) So that's my success story of how I've gotten my family's approval for my love of anime. It really does depend on a person's taste, but if they're willing to respect, or even admire the work put into an anime movie or television show, they won't question why anyone likes it--parents included.
Though it does help to have at least some knowledge of the subject so you can help clear up any and all misconceptions and answer questions--as well as the Japanese culture. My mom asked more questions than I can count about the culture more-so than the anime itself, if only to clear things up/make the scene more understandable. She knows a bit about the culture from what she remembers from an acquaintance from school who was Japanese, but considering that was years ago and Japanese perspective on Western society and people have changed since then...