I think that is a invasion of privacy, and while I think you should of course respect your parents, start clearing your search history. If that happened to me, I would be very mad
but idk it's up to you. I think in situation like that, it's best to keep the secret, as that could have been a massive em easement for you. That said, if you see a good opportunity, when you are more sure of yourself of course, it might not be that bad. You may be pleasantly surprised by their reaction-I haven't told my parents yet but my ULTRA conservative dad actually said he supports
LGBT rights, which is a massive relief
. But I would start looking for subtle clues too, Maybe even tell you a fake friend from school come out and judge their reactions? idk but of course it's all up to you.
And sorry I do tend to ramble and have really no right to be giving advice. Good luck