Actually, I've always thought that there were heavy implications that Natsuki and Yuri do have feelings for each other, but the "game" forces them to fall for the MC (if the player goes down their route). I thought that there was a lot of dialogue and even some poems that kind of pointed towards that, but I've never seen anyone else bring this up, so maybe I'm just crazy.
As for what BlueBerry said, going down Sayori's route in act I and a scene in act 4 show Natsuki and Yuri reconciling with each other and growing close. There are also multiple lines of dialogue sprinkled throughout acts I and II that suggest that Natsuki and Yuri actually want to get closer to each other, but end up fighting because they are too awkward.