don't get any big ideas, they're not going to happen...I didn't have to come out of the broom closet. I straight up told my Mom that I was interested in Paganism. A few days later, she took me out book shopping. Years after that, I got her interested in the subject, herself. She's always been keen on learning new spiritual philosophies.
So I can't really offer much advice on the subject. I don't understand how anyone could have such trouble... I understand that they do, but "why" is beyond my brainmeats.
Generally, though... I think the person is alone on the matter. You (the reader in general) know your parents best, so you are the only one who can say how to talk to them. There's no one-size-fits-all formula with parents, because they're all very different, very individual people, with their own dynamic with you (which might even differ with the dynamic they have with a sibling of yours). So just imagine their reaction, rehearse for it, and plan a back up/escape plan in case things go crappy. If push comes to shove, you (the general reader) can stay with a friend for a while til the folks cool off... or hell, there's always Child Protective Services for the underage if things go REALLY hinky. I mean, just know the contact numbers. You can't ever be too prepared, you know?
Another option... just don't lip it until you're on your own two feet by yourself. Pagan practices and learning doesn't have to be physically obvious, so it is feasible to squeak by in silence 'til you build a comfort-zone of your very own.
...you'll go to hell for what your dirty mind is thinking.