I'm most surprised that Shou had such strong feelings on the matter. I wonder why. It's not like she cares what people think. Well, she does, but I mean, she doesn't care enough to change her behavior, so this shouldn't be any different.
She might be trying to protect Umi from her friends' potential response.
I concur with this view. Rereading back the earlier chapters, it appears to be Umi who's more terrified of people finding out that she likes girls, tho she did asked a weirdass question to one of her friends.
Shou seems to fear her own weirdness affecting Umi's overall rep with her friends, Shou had few times pointed out that Umi has many friends, hence Chap 13 where she sort of suggested a break-up thinking Umi is better off without her. Shou wasn't bothered that they are both girls.
The girl in Shou's room had repeatedly commented about how Shou keeps seeking out Umi, which likely made Shou more self-concious about her being with Umi.