I'm pretty open about it - to a certain degree. As art historian specialized on Middle Ages and Renaissance, I have a perfectly understandable interest in the history of emblems, symbols and the development of hand-painted vs printed cards. When I teach basic things like Evangelists' symbols, I always mention the World card, and when I show Breughel and Vermeer, I compare them with Temperance. So my students at least know that I know the cards.
My family is super-rational and probably think I'm nuts but I've always been the purple sheep so I don't really mind. They know I love Patience cards, playing cards, Tarot cards, and that I'm really interested in the topic. They don't know how much, and I didn't tell them that I work and earn money with tarot. My mother would think it's degrading and I should rather put my energies into my (non-existing) academic career. So I don't tell her.
My idea of becoming more professional, giving courses and advertising my services openly doesn't get off the ground because I know my mother would be mortified if she knew it's beyond an academic interest. For her and my whole family, that's all bullshit, charlatanerie, the worst kind of exploiting peoples' willingness to believe.
My husband's family is much more open, they're really interested and look at my decks and ask questions. My children of course know and for them, it's simply a part of who and what their mother is. My eldest son asked me to show my Thoth to his girlfriend because that's "Mama's cards" for him, and reminds him of me. I also read for her and she really liked it. And they're both very rational people, so is my husband, but they all understand cards are not anti-rational but trans-rational, if I may coin a new word
I'm glad I didn't meet religious bigots - I don't know how I would react, probably badly.