I've read the Light Novel and promise, Rei becomes a lot less weird as time goes on. In the beginning she's absolutely portrayed as this one-sided, obsessive/creepy lesbian (which sucks, im saying this AS a queer person, this early portrayal super blows).
It's not elaborated here in the manga, but in the LN Rei makes it clear while her feelings for Claire are genuine, the dopey obsessive behavior is done more to get a rise out of her than be an "actual" stalker. Rei repeatedly says she finds Claire's flustered reaction cute. This is made even more stark in the novel when a woman who ACTUALLY intends to be a creep to Claire shows up. After that arc, Rei dials back the behavior a lot. Also, as their relationship develops and they become closer as friends, Claire not only reciprocates her advances but Rei teases her less as they become more genuine w/ each other. So if you're worried about this being The Whole Story, don't worry. It's def not!!!!!!
If you're uncomfortable w/ this and need some content warnings please feel free to reply to this or DM me, I'm more than happy to elaborate if you need details or provide you the LN chapter numbers in order for you to skip/investigate on your own.
I ADORE this LN/manga, I think Rei and Claire are a fantastic gay couple, but I would be remiss if I didn't acknowledge how icky the early story is with its portrayal of Rei's behavior both as a fan and as a queer person who is sensitive to negative portrayals of LGBT characters in media.