Can my parents really see everything and everyone I talk to online?

Okay so recently my mom comes up to me and says "You're dad knows web specialist, they'll find out who you're talking too and what you're doing on video games or the internet and ect…" (Context, they don't want me talking to my boyfriend anymore cuz he's not our religion) so like… Can they actually figure out if I'm talking to him on Snapchat or discord? Or video games like Overwatch and steam? Like on my laptop or IPhone?

I think they can, maybe you should use the computers at the library if you don't want your parents into your business like that