I have no problem with people rooting for multiple schools in the state. Honestly, whether it's Nebraska/Creighton, Nebraska/UNO, Creighton/UNO, it's fine with me as long as you're consistent about it. These rivalries are mostly fabricated fan contrivances.
What I do dislike are the people who root for Nebraska in football (probably referring to the team as "we" in the process), but then claim to hate the basketball team because of their love for another school (typically Creighton). They are typically the ones also trying to fuel these pseudo rivalries.
I root for Nebraska in all sports and as an alum, I root for UNO in everything. On those rare occasions NU and UNO meet head to head, I typically cheer for UNO. That doesn't mean I'm rooting against Nebraska or revel in them losing to UNO. I just have to pick, and I'll typically go with the underdog and a school that I happen to have a deeper attachment to. Still, as soon as Nebraska beat UNO last night, I could appreciate their effort and move on rooting for both teams.
I just don't think a person can claim to love one sport within an athletic program and hate another. Those things just don't mesh if you ask me. I could never hate any team wearing a logo I claim to love.