It seems to me that he
is being himself and enjoying what he likes, or else he would've given up anime out of shame. I don't think that it's weird to have interests that family members don't know about (at least if we're talking about family that we no longer live with). I like lots of things that my family doesn't know about... like Kurosawa films. They're not really into foreign films, so why would I ever talk to them about them? Similarly, I like Carly Rae Jepsen's music, but my family has very different tastes in music, so there's no reason to bring it up. It's not that I'm insecure about my tastes. I'm just a private person who doesn't share things unless there's some reason to. I'm not one of those people who will talk your ears off about subjects that I care about but you don't.
Also, I think that there's a difference between keeping something to yourself because you're insecure and keeping it to yourself because you don't want to be rude
.