This seems to be quite common among family. It might be that people have gotten so used to you that they just see your AS traits it as a personality quirk. Or it could be that you feel safer around them so the traits aren't as pronounced. I know that's the way it is with me. I can look people I'm close to (some of my family, close friends) in the eye when I talk to them sometimes, but I can't with most other people. My family is also used to me memorising things and info dumping on them every time I get interested in something new; other people definitely aren't so keen.
Besides, like others mentioned, there's the stigma associated with being on the spectrum. People don't usually want to be associated with that, and quite often, they will probably think that you'll be better off not doing so either. People, like my parents, tend to view being on the spectrum in a negative light. Like when I talk to them without eye contact, they'll often call me autistic just as a way of insulting me (because they think I'm being deliberately rude), and not because they think that I'm really on the spectrum. It's a bit like equating being autistic/an aspie with being stupid, and when you say you might have AS, what they seem to hear is that you might be severely abnormal in some way. It's unfortunate, but from what I've experienced, it's pretty common.
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Aspie score: 153 of 200
NT score: 60 of 200