I feel like I'm in a similar situation as you, except I would be the other girl who wants an exclusive relationship and isn't keen on the other girl.
of course, for me, I'd like to meet her(the other girl in what I guess is a V for us) just to see what she looks like and maybe get a first impression of her, but I definitely do not want to be friends with her because I see her as competition almost. Maybe she's feeling the same? Like you might pose a risk to her? It's easier to ignore the existence of another relationship if it's not in your face. Out of sight, out of mind.