She isn't afraid of her gf finding out anything. She's afraid of the whole school finding out that she's dating another girl.
I think Yuni is afraid of her gf finding out too? Nanase’s backstory basically indicated that she and her former flame were ostracized when rumors popped up in her old school? Hence why Nanase isn’t as touchy with Yuni in public.
Yuni is probably afraid that Nanase will leave her if anyone else finds out or will leave because she’s been putting their stuff on blast on social media.
On a side note, totally agree with people. If you’re too busy and have goals/dreams that you know will take most of your time it’s probably not a good idea to have a girlfriend who doesn’t have the same mindset. But they are teenagers so I get there’s a lot of error by to be made by all parties. They wanna push certain limits and think “love will conquer all”…
Though I wouldn’t be surprised if Nanase is just a really good manipulator? Telling Yuni stuff to placate her and keep her so she’ll have someone to booty call. Don’t know how despicable things are going to get but fun ride so far.