I would let the two of them see my internet history. I know that I have been relatively clean with the things that I do on my on the internet. It is all about business with everything that I do on the internet.
I don't mind sharing my internet history. Sometimes I wake up in the middle of the night with something that clicked into my brain and I needed an answer right then and would search on my phone. But that's just me and my busy mind needing to research things. A lot of my searches aren't even for me, but for other peoples' needs!
My parents and my boss are free to see my internet history. I can freely show them all the videos I watch, all the chats I have had with Generative AI and my entire browsing history. I am clean as a bird.
Definitely my parents, I would be afraid that I might lose my job for things I might have looked up in the past or said online when I was younger lol. My parents wouldn't even care about my activity, they might mess with me but won't be truly disgusted or anything lol.